#sphere; convex

[mycoblogg]

HORROR WEEK- FOTD #144 : apple bolete! (exsudoporus frostii)

the apple bolete (also frost's bolete) is a mycorrhizal fungus in the family boletaceae >:-) it typically grows near the hardwood trees of the eastern US, southern mexico & costa rica. it was chosen for horror week due to its appearance being reminiscent of muscle tissue !!

the big question : will it kill me?? nope !! however, although they are edible, they are not recommended for consumption as it is quite easy to confuse them with other red boletes. ^^

e. frostii description :

"the shape of the cap of the young fruit body ranges from a half sphere to convex, later becoming broadly convex to flat or shallowly depressed, with a diameter of 5–15 cm (2.0–5.9 in). the edge of the cap is curved inward, although as it ages it can uncurl and turn upward. in moist conditions, the cap surface is sticky as a result of its cuticle, which is made of gelatinized hyphae. if the fruit body has dried out after a rain, the cap is especially shiny, sometimes appearing finely areolate (having a pattern of block-like areas similar to cracked, dried mud). young mushrooms have a whitish bloom on the cap surface.

the colour is bright red initially, but fades with age. the flesh is up to 2.5 cm (1.0 in) thick, & ranges in colour from pallid to pale yellow to lemon yellow. the flesh has a variable staining reaction in response to bruising, so some specimens may turn deep blue almost immediately, while others turn blue weakly & slowly.

the tubes comprising the pore surface (the hymenium) are 9–15 mm deep, yellow to olivaceous yellow (mustard yellow), turning dingy blue when bruised. the pores are small (2 to 3 per mm), circular, & until old age a deep red colour that eventually becomes paler. the pore surface is often beaded with yellowish droplets when young (a distinguishing characteristic), & readily stains blue when bruised. the stipe is 4 to 12 cm (1.6 to 4.7 in) long, & 1 to 2.5 cm (0.4 to 1.0 in) thick at its apex. it is roughly equal in thickness throughout its length, though it may taper somewhat toward the top ; some specimens may appear ventricose (swollen in the middle). the stipe surface is mostly red, or yellowish near the base ; it is reticulate — characterized by ridges arranged in the form of a net-like pattern."

[images : source & source] [fungus description : source]

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Finals)

Propaganda

Truncated Icosidodecahedron:

Also called the Rhombitruncated Icosidodecahedron, Great Rhombicosidodecahedron, Omnitruncated Dodecahedron, Omnituncated Icosahedron

Archimedean Solid

Semiregular

Dual of the Disdyakis Triacontahedron

It has 12 regular decagonal faces, 20 regular hexagonal faces, 30 square faces, 180 edges, and 120 vertices.

It has the most edges and vertices of all platonic and archimedean solids.

Of the vertex-transitive polyhedra, it fills up the most of the volume of the sphere it fits in (89.80%).

It is not actually the shape you get when you truncate an icosidodecahedron, although it is topologically equivalent.

It is the mod's favorite three-dimensional shape.

They made a void truncated icosidodecahedron and it's glorious. I had one for a while, it's hard to turn because of alignment issues, especially the decagonal sides. Fun puzzle tho, never did figure out how to permute the last layer...

Image Credit: @anonymous-leemur

Regular Icosahedron:

Platonic Solid

Regular

Dual of the Regular Dodecahedron

It has 20 regular triangular faces, 30 edges, and 12 vertices.

Image Credit: @etirabys

[shdo-xplosion]

INTRO: BEGIN TRANSMISSION

warnings: general warnings on the MASTERLIST! this chapter contains elements of fear, language barriers, and choking (not in a fun way) 1.4k

notes: this is just the beginning ( •⌄• ू )✧ plzplz tell me what you think!!!

ₓ˚. ୭ ˚○◦˚.˚◦○˚ ୧ .˚ₓ

“You sure you’re ready for this?”

Securing your helmet, you glance at Shinsou through the convex lense and laugh. “A little late to be asking that, don’t you think?”

“Just giving you the chance to hide under your blankies until this is all over,” he smirks.

“You mean hang out in the ship for the next two years? Think I’d die of boredom.”

When you’d first joined the crew you probably would have been able to entertain yourself for that long, exploring all the nooks and crannies of Hermes, but after years of learning all its secrets most of the mystery is gone.

“Just remember I gave you an out.”

“No outs allowed,” Kendou pipes up, voice distorted by her helmet speaker. “We’ve been preparing for this for years. We’re all ready.” She flexes both of her bionic hands, a subtle indication that she’s just as nervous as the rest of you.

The main door of the ship slides open in front of you, and Kendou leads the way out of the familiar territory and onto the shuttle platform, seven other crew mates following.

You’re all a very long way from home—light years away. The people you’ve left behind have all aged many years while you slept through the journey. Your entire home planet has changed drastically. And it’s only going to keep changing, keep degenerating. It’s why you’re here now.

Nobody knows exactly how to say this world’s name, but they sent a simple message that included something of an alphabet. Shinsou, your language expert, translated as best he could.

“The closest I can get as far as pronunciation is Destro, but they don’t really have vowels, so it’s more like dsst-ruh,” he tried to explain.

“Sounds a lot like ‘destroy’,” you had pointed out, trying to laugh off your unease.

Monoma snickered while throwing an arm around your shoulders. “Don’t worry. I’ll protect you if anything spooky happens.”

It’s hard to get that out of your head as you make your way down the catwalk. Don’t look down, don’t look down, you repeat to yourself. The landing port and platform seem to be surrounded by nothing, a single lit up construct in the darkness. Though the station is in view, it looks very small.

Every step closer makes your stomach crawl higher in your throat, and by the time you make it to the massive doors that will grant you entry, you feel like throwing up.

“It’ll be fine,” Kendou’s voice sounds through her speaker. “We’re doing this for all of humanity.”

“You sound very brave,” Monoma snorts.

Shinsou, unwilling to wait apparently, steps forward and pounds on the door, unfazed when a large sphere drops out of nowhere, red light pointed in his face.

“Probably a camera,” he says.

“Or some kind of laser that’s about to melt your face off.”

“Helpful, Monoma. Very helpful,” you comment sarcastically.

Shinsou slowly holds up a gloved hand for the supposed camera to see, then speaks clearly: “Planet Earth. Humans.”

You don’t know what good it will do since they don’t speak your language, but whoever or whatever is on the other side of the doors must understand enough to know that you are not invaders but visitors.

The grind of the doors opening echoes in the abyss, a bone-chilling sound. You rest your hand on the gun at your hip, eyes widening as you’re finally able to see what lies ahead.

A handful of strangers are waiting for you, and you try to take in as much as you can in a short amount of time. Humanoid in stature aside from size, the same number of limbs, even their faces look similar to yours. But their eyes are different—sharp, the sclera (or what you assume to be), filled in red rather than white. What could be hair looks coarse and glitters in the light. There are markings on their cheeks and noses, different colors, and their skin, ranging in human hues, is smattered with scales.

Shinsou has his tablet ready, projecting a hologram of their alphabet so that he can point to the different letters that spell out ‘hello’ followed by ‘peace’.

The alien at the front of the group nods, grunts, then raises a hand and points at the device to spell something else out. Shinsou’s tablet collects each letter and translates them so that he can look at the rest of you and relay, “decontamination. I guess that’s the first thing we need to do.”

After a few more typed exchanges, the possible leader turns and motions your crew to follow his.

They’re taller than all of you, averaging anywhere between 7 and 8 feet, but the similarities are a little baffling to you. You suppose if their planet is anything like earth, the shared traits make sense. Maybe they’re taller because this world is richer in oxygen. Maybe their longer fingers have more webbing in between because they spend more time in water. Maybe the serrated teeth one of them flashes at you are for tearing apart tougher meat.

Or for ripping the throats from their prey.

You force a smile at the one looking down at you, hoping it isn’t an aggressive gesture. The way it puffs its chest out and shows more of its teeth makes you think it might be trying to smile back.

Despite your crew outnumbering theirs by three, you can’t help but feel watched, like there are many many more eyes on you that you can’t see. It makes your skin prickle, and you keep your hand close to your gun.

Another, smaller set of metal doors opens, and once inside the creature in charge points toward a room that looks to be made of glass. You can see through the walls, spot dozens of fixtures that resemble sprinkler spickets. Decontamination.

“Are we sure this is a good idea?” you ask Kendou. “We don’t know what they’re going to use on us. What if it’s acid or something?”

Her jaw is set, eyes trained on the room you’re being led to.

“It won’t be. If they wanted to hurt us, they wouldn’t have offered their help,” she reasons.

You’re not so sure about that.

“Suits off,” Shinsou says, holding up his tablet as if anyone else can read it. “There’s enough oxygen that we’ll be able to breathe.” He takes his helmet off to demonstrate, and you’re relieved when his head doesn’t explode on the spot. “It’s sort of like breathing at a high-altitude, though, so be ready for that.”

You have to fight every one of your instincts in order to strip yourself of your suit and helmet—your protection. It’s your life support when you’re traveling the stars. You feel completely vulnerable without it.

In nothing but underclothes, the 8 of you walk into the strange chamber. All you can think is that these might be the last few breaths that you ever take. This could all be a trap, no large step for mankind.

The door closes, and you stare through it, catching the red eyes of the alien who had been walking next to you. You think you see his mouth begin to pull up on one side just as a substance begins spraying from the spickets all around you.

It isn’t liquid nor is it gas—more like some kind of powder that coats your mouth and makes you cough. If it was hard to breathe before, it’s getting impossible now, this stuff clogging your throat and the throats of those around you.

The room is filled with violent hacking. Monoma vomits next to you, his watery eyes caked with whatever this is.

You wave a hand in front of your face in an attempt to dispel some of the flakes floating around you, searching for Kendou, for Shinsou, for an escape as you realize with terror that your gut instinct has been right. You never should have walked into this place, never should have taken one step off Hermes. This was a fruitless mission. This was arrogance, humans thinking you deserved to be helped.

Your vision is almost non-existent, and it feels like every inch of you is caked with whatever poison is pouring down on you. You bang on the wall with a desperation you’ve never felt before, screaming pleas you know the creatures don’t understand.

We’re dying. I’m dying. We came all this way to be killed.

The smiling alien watches you as you grow more and more light-headed. Whatever you’re inhaling burns your lungs, your mouth, the very inside of your skull.

The last thing you see before blacking out is the smiling alien’s split tongue running over its lips, a hungry beast waiting for its next meal.

ₓ˚. ୭ ˚○◦˚.˚◦○˚ ୧ .˚ₓ

2023©️shidou-x. please do not plagiarize or repost my work to any other platforms.

[infin-8-morphosis]

The Y Malom (Literally, Cyan Bigtooth) is a species on Ternual, found primarily along a coastal plain. A middlingly sized mesocarnivore, that gets by on ambush predation and scavenging. On Ternual, this completely independent evolutionary tree has converged on something familiarly canine-like. At first look.

As you can see, their lower jaws can split slightly. They're not actually all that powerful though, since they mostly bite down with their top jaw, as their spine is on the bottom! Basically, they open their mouth like those bins with the pedal, you know the ones. This is honestly really inconvenient for hunting, but they're stuck with it! This is one reason for the enormous teeth; its imperative that if they bite something, they really, really bite it. In combination with the slight opening of their lower jaw, they can open their mouth reeaaally wide.

Their nose probably looks fairly typical at first glance, but its actually a single nostril on the top jaw, and two pseudo nostrils on the bottom jaws. (Internally, they join together, only a bit of flesh separates them, so they can still inhale while the jaws are out) They branch out to the eyes as their sensory lines, which are repurposed lateral lines. They keep the eyes and noses moist, detect air pressure, balance, and enhance the senses, particularly smell and chemical detection.

Along the inner mouth, parallel to the lines, are the 'teeth'. Comparatively its more like a beak, with tooth-like serrations. It grows out of the bone, coated in a hard sheath. While the inner part stops growing, the sheath is shed periodically and regrows. As such, they remain extremely sharp, and are much less prone to infection and decay.

Notice that its eyes are concave, shaped like a bowl, rather than a sphere. (It still has a convex cornea though, that covers it entirely, and is much tougher) I can't really speak on the effectiveness of it, but it is an ancestral trait; its stuck with it. It can actually rotate them slightly, but not much. Like birds, it alters its visual range more so by moving its neck. It probably stabilises its head like one too!

Speaking of, on its neck is a cobra-like frill. The inside of it is lined with glands, which collect energy from the surroundings, and store it. This energy is specifically ice/cold energy, which it can release through its teeth or claws (mostly teeth) for a freezing bite. If the fangs weren't enough to keep prey down, injecting the energy into somethings' muscles would almost certainly make it unable to move.

Its neck is also pretty flexible. However, since the spine is on the bottom, its range of motion is sort of flipped, being able to swing its neck very far backwards, but not as much forwards. It would struggle to look in between its legs, but would comfortably curl its neck onto its 'back' to rest!

Said legs as you can see are pretty odd looking. Anatomically there's not actually much to say here; I see no reason they'd function any different from our legs! They have a different range of motion, and probably a more horse-like gait, on account of the long 'wrists'.

They have 3 toes, which are symmetrical. Underneath the skin however are probably vestigial extra toes, from its ancestors, who had a toe on each joint. You will see what I mean in my other creatures someday. :]

Their colouring probably seems very out there, but in its natural environment, it blends in perfectly. It has countershading on its underside and feet, to blend in the shadows and the lighter soil, while the varied pinks blend into equally pink foliage. The white spots on its back are also to blend in, as dotted throughout its natural habitat are round white 'flowers', sort of like puffball mushrooms.

(Old art obviously but for a visual... look how far my boy has come)

Its tail is split, as you can see. Actually technically its entire spine is, but the two halves are long fused. Only the tip, which house the ears, remain separated. There's not much to say here, they're just ears! They're derived from a tail fin, and function much the same as ours, aside from the odd location. Their tail is very flexible, so it can turn in any direction to listen.

To finish, I think you'd love to hear that it reproduces entirely with its mouth. As its oceanic ancestors were mouthbrooders, it evolved to do much the same on land. Aside from the location, they aren't too inventive. Lots of posturing and displaying, fluid exchanging, and in a few months, a moderately developed puppy gets vomited out. They aren't parental much, but the pre-adults live in the forest rather than the open plains, to avoid competition and make use of different niches. Oh, the same goes for digestion. Food in... Food out. Probably why the split jaw stays around, opening it makes things much less messy.

And that's the guy! Thanks for reading. :]

[thepastisalreadywritten]

Galileo's first telescopes 🔭

Galileo's (1564-1642) early telescopes, which he constructed in the early 17th century (around 1609), marked a major advancement in observational astronomy.

These telescopes were based on the principles of existing Dutch telescopes, which had been developed by spectacle makers in the Netherlands.

These early telescopes, known as refracting telescopes, utilized a combination of lenses to gather and focus light, magnifying distant objects. Galileo further refined and improved their design.

The design of Galileo's telescopes typically consisted of a convex objective lens (the primary lens) and a concave eyepiece lens (the secondary lens).

The objective lens collected light from distant objects and converged it to a focal point, forming an image.

The eyepiece lens then magnified this image for the observer to see.

Galileo's telescopes had relatively low magnification power compared to modern telescopes, but they enabled him to make groundbreaking observations.

With these instruments, he made a series of significant discoveries, including:

Observations of the Moon

Galileo observed the rugged, mountainous surface of the Moon, challenging the prevailing belief in its perfect smoothness.

He also noticed the presence of craters and other lunar features.

Sunspots

It revealed that the Sun was not a perfect sphere and that it rotated on its axis

Discovery of Jupiter's moons

He observed four of Jupiter's largest moons, now known as the Galilean moons.

Their discovery provided evidence that not all celestial bodies orbited the Earth, challenging the geocentric model of the universe.

Phases of Venus

Galileo observed the phases of Venus, which he interpreted as evidence for the heliocentric model of the solar system proposed by Copernicus.

This observation suggested that Venus orbits the Sun and not the Earth.

Observation of Saturn

Galileo observed Saturn and its rings, although he was not able to discern the true nature of the rings due to limitations in his telescope's resolving power.

Galileo's telescopes revolutionized astronomy by providing concrete evidence that supported the Copernican heliocentric model of the solar system.

His observations and discoveries contributed to a profound shift in our understanding of the cosmos and laid the foundation for modern observational astronomy.

Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath.

He was born in the city of Pisa, then part of the Duchy of Florence.

Galileo has been called the "father of observational astronomy, modern-era classical physics, the scientific method, and modern science."

[art-mirrors-art]

M. C. Escher - The Sphere (Self-portrait in a convex mirror) (c.1920)

[academicstraykittie]

The Cloud by Percy Bysshe Shelley

...............................................................

I bring fresh showers for the thirsting flowers,

From the seas and the streams;

I bear light shade for the leaves when laid

In their noonday dreams.

From my wings are shaken the dews that waken

The sweet buds every one,

When rocked to rest on their mother's breast,

As she dances about the sun.

I wield the flail of the lashing hail,

And whiten the green plains under,

And then again I dissolve it in rain,

And laugh as I pass in thunder.

I sift the snow on the mountains below,

And their great pines groan aghast;

And all the night 'tis my pillow white,

While I sleep in the arms of the blast.

Sublime on the towers of my skiey bowers,

Lightning my pilot sits;

In a cavern under is fettered the thunder,

It struggles and howls at fits;

Over earth and ocean, with gentle motion,

This pilot is guiding me,

Lured by the love of the genii that move

In the depths of the purple sea;

Over the rills, and the crags, and the hills,

Over the lakes and the plains,

Wherever he dream, under mountain or stream,

The Spirit he loves remains;

And I all the while bask in Heaven's blue smile,

Whilst he is dissolving in rains.

The sanguine Sunrise, with his meteor eyes,

And his burning plumes outspread,

Leaps on the back of my sailing rack,

When the morning star shines dead;

As on the jag of a mountain crag,

Which an earthquake rocks and swings,

An eagle alit one moment may sit

In the light of its golden wings.

And when Sunset may breathe, from the lit sea beneath,

Its ardours of rest and of love,

And the crimson pall of eve may fall

From the depth of Heaven above,

With wings folded I rest, on mine aëry nest,

As still as a brooding dove.

That orbèd maiden with white fire laden,

Whom mortals call the Moon,

Glides glimmering o'er my fleece-like floor,

By the midnight breezes strewn;

And wherever the beat of her unseen feet,

Which only the angels hear,

May have broken the woof of my tent's thin roof,

The stars peep behind her and peer;

And I laugh to see them whirl and flee,

Like a swarm of golden bees,

When I widen the rent in my wind-built tent,

Till calm the rivers, lakes, and seas,

Like strips of the sky fallen through me on high,

Are each paved with the moon and these.

I bind the Sun's throne with a burning zone,

And the Moon's with a girdle of pearl;

The volcanoes are dim, and the stars reel and swim,

When the whirlwinds my banner unfurl.

From cape to cape, with a bridge-like shape,

Over a torrent sea,

Sunbeam-proof, I hang like a roof,

The mountains its columns be.

The triumphal arch through which I march

With hurricane, fire, and snow,

When the Powers of the air are chained to my chair,

Is the million-coloured bow;

The sphere-fire above its soft colours wove,

While the moist Earth was laughing below.

I am the daughter of Earth and Water,

And the nursling of the Sky;

I pass through the pores of the ocean and shores;

I change, but I cannot die.

For after the rain when with never a stain

The pavilion of Heaven is bare,

And the winds and sunbeams with their convex gleams

Build up the blue dome of air,

I silently laugh at my own cenotaph,

And out of the caverns of rain,

Like a child from the womb, like a ghost from the tomb,

I arise and unbuild it again.

[marzghost]

Red Queen au with everyone from hermitcraft and empires + Martyn, Bigb, and Skizzleman anyone? I know this is such a niche little thing but god do I love this book series and what type of person would I be if I didn't put my little block men into it. 👀

Like imagine it if you will. Scar as Cal ,Grian as Mare, and Cub as Maven (I'm living for the convex drama I also have no clue who would take on the role of Evangeline but we'll cross that bridge when we get there. Thinking maybe Cleo but who knows it might change). Might make this into an actual fanfiction with Grian being born a female but identifying and passing off as a male because I can do as I please and who doesn't like the angst that comes from being forced to parade around as something you know you aren't.

if I make this a full on fanfic it'll be called The Red Blood On My Teeth Tastes Sweet On Your Silver Tongue (but our sins turn it bitter like a war over done) on AO3 but for short I'll be referring to it as the Red Blood Silver Tongue AU or RBST Au

Enjoy this snippet so you guys can somewhat see what I'm talking about. If I do make it into a full on fanfic I'll be sure to tag warnings because I know for a fact there will be a lot of misgendering and body dysmorphia since Grian will be forced to parade around as a female despite identifying as a male.

..............................................................................................

Grian was alive. Grian was alive that much he knew for a fact from the way his heart raced within his chest and his blood pulsed within his ears. He was alive when he should have been dead. His body should be nothing more than a charred clump upon the electric dome but here he was ,a mess, being watched by every important silver house there is.

He should be dead. Should be nothing more than a red and black stain upon the electric shield but instead he laid upon the ruined ground of the arena with his once beautiful new uniform burnt and smoking from the electricity that had been coursing through his body not too long ago. He should have felt pain when he fell down to what should have been his untimely demise but no. Instead of feeling anything he thought moments like this should entitle he felt more alive than he's ever felt before. It was like a blindfold had been lifted from his eyes and as he stood to his feet dazed and confused, wide dark eyes locked with intense and shocked lime green ones and like a fool he lifted his hand and waved with a nervous smile crossing his thin lips before saying, "Uhh, hi?"

That was all it took for the dam to break. The metal spheres the ginger and been controlling flew out towards him and in some sad attempt to save himself Grian quickly outstretched his hands in front of himself. One moment Grian was yelling wait at the top of his lungs and the next lightning was coming out of his open palms saving him from yet another untimely death. If the silvers hadn't been gasping before they sure as hell were now.

Then, like thunder, the king's voice cut through the air. "Guards! Seize him!" He commanded and like flipping a switch the guards all around snapped into action. Now Grian was no fool. He knew when to leave and as his eyes landed on his ticket out of the arena he took it. Running past the stunted girl he slid down through the lifted platform that had been used to bring up all the other ladies into the now destroyed area and landed down in some brightly lit hall. He could feel the energy powering each lightbulb but just as he focused on one it would explode in a flash of light and glass. Panic pushed his legs forward as lights exploded behind him ringing like alarms wherever he went and it wasn't long before the sounds of armored footsteps accompanied his own.

Taking another left Grian found himself looking out an open window and just as he hoisted himself up onto its frame two strong arms wrapped themselves around his waist and pulled him away from his only chance at freedom. Screaming and kicking Grian turned to snarl at the fool who had captured him but stopped dead silent for when he did he was met with two now familiar forest green eyes and striking scars.

"I'm so sorry Grian but go to sleep."

Scar whispered to him and just like that Grian watched as the world blurred around him and turned black with the last thing he saw being Scar's ,no Prince Rayn's, eyes glowing slightly gold in the light of the now setting sun.

(yeet there ya go btw I know it's very close to his real name but i didn't know what other name to give him and I really liked Rayn (pronounced rain) despite it basically being his real name with only the Y and A swapping places.)

[aliencatadventures]

Black Hole and Cosmic Lensing

Once in my early youth, I watched a sci-fi movie about space travel that supposedly featured a black hole. It resembled a galaxy, which I found quite amusing—how can you see a black hole if no light can escape from it? Much later, I realized that although the depiction in the movie wasn't accurate, and yes, we certainly can't see the black hole itself, there are still many fascinating phenomena around it that can be observed. So, what exactly can we observe?

First, imagine Saturn with its majestic rings. Then, imagine this Saturn turning black, becoming invisible—and you'll get the picture. There are luminous rings rotating around something that, in reality, we cannot see. But it's definitely there. These rings, or more accurately, the matter drawn in by the black hole, spin at tremendous speeds and are located in the equatorial plane—just as in any galaxy formed around any massive celestial body. Unlike the tranquil, icy rings leisurely circling our native gas giant Saturn, this matter is accelerated to nearly the speed of light. It may be dense and heated near this celestial body and becomes more sparse and slower farther away. Another way to visualize it is like a whirlpool, only much faster.

But in the picture (below), it doesn't quite resemble rings. It looks more like a strange, faceless smiley wearing a hat, reminiscent of what some viewers might have seen in the movie 'Interstellar.' The reason is that space is distorted so much, so what lies behind this celestial body appears partially above and partially below it. The image seems almost turned inside out. Thus, the depiction is akin to Saturn's rings, if they were reflected in a curved mirror, or more accurately, viewed through a powerful lens.

I highly recommend clicking on the link on the video (below) to see it in action - it's absolutely spectacular!

Also, if you haven't seen the movie 'Interstellar,' I strongly suggest watching it. A group of scientists, including Kip Thorne, participated in its production. Thorne even wrote a book titled 'The Science of Interstellar' with scientific explanations. He explains how the film crew aimed to create images and visualizations as close as possible to what is actually known in science, or at least to use real scientific hypotheses. For the visualization of the black hole, they employed real scientific models, and the visuals were based on the latest scientific understanding. This approach was validated by the recent actual photograph of a black hole.

In this visualization (below), it’s easy to observe dynamically why the rings around a black hole take on such a peculiar shape. The image displays a computer model showing how a black hole would appear if it passed in front of a distant galaxy. Note that the galaxy itself remains unaffected; it is far away, and nothing is happening to it. It's just the image of the galaxy that changes - it resembles what you would see if you took a thick, convex lens and moved it across the backdrop of that same galaxy or a simple geometric pattern. If you have such a lens or a glass sphere, try this experiment. It’s a straightforward way to help understand this phenomenon

So, the biggest difficulty in understanding is that the picture appears static to us. As soon as you see it in motion, there's a moment of recognition of the phenomenon, and then it's no longer a problem to understand why you see rings both around the shadow of the black hole and above and below it.

Furthermore, the ability to view images dynamically also facilitates the discovery of new black holes. When astronomers notice that an entire sector of a previously familiar scene begins behaving strangely — with stars moving erratically or stretching into curved lines, and the image becoming blurred — it strongly indicates the presence of an invisible object traveling between us and this background scene, distorting the image. But we'll discuss this in more detail next time. Stay tuned!

[frightingly-intruguing-theories]

The shape wars

NEWCOMERS

Tungsten cube 2 apparently sacked glitchy a question that they did not answer. Then tungsten cube 6 joined in, confusing glitchy cause it them to thing cube 6 was in fact cube 2 or of friend of them. Then cube 5 joined, saying that there is multiple people in on this. Cube 3 said “we are many” them was promptly sent to the corner.cube 4 said that there was 7 of them, also being sent to their corner. Cube 8 joined, informing glitchy that there was infant 8 cubes. Then the sphere anon joined, already on attack mode saying that they were against all 8 cubes. Octahedron anon joined asking “the f*ck”

THE WAR BEGINS

Cube 6 says “Lmao imagine being a sphere”, then was sent to their corner for bullying. Then triangular prism joined, peaceful at first. Then sphere anon comes back saying “at least I can f*caking move around tungsten cube 6”. This started the war. Sphere anon didn’t even wait for a reply before saying “bro really said be there [or] be square and you didn’t show up”. This sick burn fuelled the cubes rage. Octahedron anon attacked triangular prism anon, saying that they had a six pack in comparison. Sphere anon said the straw that broke the camel’s back “imagine having sides?? Like you can’t even move around on your own.”

Cube 6 came back from the corner swinging “shut up sphere I have 600 little legs we all do you need a slight slope to move” cube 6 said, even though it was a bit nonsensical sphere anon was still out for blood. Saying that they have hands, and that cube 6 was about to catch them. Then cylinder anon joined, saying that they can stand and move around. Sphere anon decided that it would be a good idea to team up to take on the behemoth that the cube empire was, so they asked to team up with cylinder anon. Then cube 10 joined. Then with one swoop cube 27 ( I have no idea where the other 16 are) joined, and upped the ante saying that if sphere talks again, they will shoot them.

THE BATTLE

Sphere anon said that they had nukes, tanks, anti tank weapons, and guns. Icocidodecahedron joined and said “imagine only having six sides, losers”. Sphere anon was tired of cube 27s silence and said “tungsten cube 27 has gone REAL f*cking quiet now, go p*ss your pants p*ssbaby”

IDK EVEN MORE

7 joined cause they killed and ate 56 people, cube 8 said “yo ball boy shut up or we’re launching the f*cling sun at you” rhombus joined when it was to late, asking what’s going on, spher anon tried to team with octagon, I joined, 2 d shapes started with square Icocidodecahedron tried to join sphere. The cubes agreed to protect 2 d shapes. Octahedron told sphere to get some vertices. Sphere accepted Icocidodecahedrons offer. Cube 8 threw the sun. Octahedron and sphere fight over Icocidodecahedron. A sh*t ton of people join. Square wants peace for all. Someone killed square by crushing them like a bug. Medical cube comes to save square. Square gets revived.

Icocidodecahedron “accidentally” pushes medical cube down the stairs. Regular non convex great icosahedron anon asked to be a shape. Square asked if they were at peace yet (they were not). Lone star joined. Lowercase anon asks square anon to rule the world together. Medical cube is now mad. Square accepts lower case anons ask, only if they do it peacefully. 7 wants to eat medical cube truacontahron tries to stay out, but can’t. Lower case anon says some romantic stuff. Cube 1 says to stop the fighting, so lower case anon and cube can be together

THE MARRIAGE

Officiant anon says that they have word of a proposal. Red anon agrees on peace. Cube 3 says that they need to make a wedding. Octagon becomes the flower girl. Lower case anon proposes, square says yes. Lower case anon says they will take over and unite the shapes, colours letters, and everyone else. Many people want to be the flower girl. They get married happily ever after.

DEATHS

1. Square (2 d gang) last words “This is it for me I guess… it was nice knowing everyone” [REVIVED]

@glitchysquidd

[co-xeter-group]

what's the siney graph in your header?

I encourage anyone reading this to read as much or as little as they want. I hope that anyone can understand the detailed explanation, and that most math undergrads can understand most of the observations I make. The generalisations might not be so accessible all the time.

To put it tersely, its the projection of the barycentric subdivision of a tetrahedron onto the 2-sphere, visualised on a rectangle via the mercator projection.

This is closely related to Coxeter groups, the classification of polytopes, the classification of straight line Coxeter groups, the classification of regular tilings of surfaces of constant curvature, and Schl\"afli symbols.

A more detailed explanation:

Imagine taking a tetrahedron, putting a dot on the middle of each vertex, edge, and face, and connecting them all up with straight lines along its surface. This is the so called "barycentric subdivision". Then consider the origin to be in the middle of the tetrahedron, and then project the tetrahedron (and the lines we drew on it) onto a sphere. We use the mercator projection to view it like a map, but we still think of it as lying on the sphere (see below mp4 of said sphere with the barycentric subdivision drawn on it). Each face of the tetrahedron could be imagined to be coloured a certain colour, so v_2 in the diagram on my header is the vertex at the centre of the yellow face, v_1 is the vertex in the centre of one of the yellow faces edges, and similarly for v_0. These appear to be connected by curved lines, but these are straight lines on the surface of the sphere.

Assume the tetrahedron and sphere are embedded in R^3 and share a common centre at the origin.

Some interesting observations:

each of these lines we drew now gets turned into a great circle, which corresponds to a plane going through the origin

reflections in these great circles preserves the lines we drew, and correspond to automorphisms of the tetrahedron

each triangle in the subdivision has angles pi/3 radians, pi/3 radians, and pi/2 radians.

the symmetry group of the tetrahedron is S_4, where the adjacent transpositions correspond to permutations of the faces (or if you like, vertices)

the symmetric group S_4 has a presentation , where the s_i are adjacent transpositions of 4-tuples

The exponents of the (s_is_j) terms above exactly match the denominators of the angles of the triangle mentioned above

we can pick one triangle on the sphere and consider the reflections in (the faces corresponding to) its edges, denoted s_0, s_1, and s_2. These reflections permute the coloured faces of the tetrahedron, or if you like, its vertices.

we can repeatedly apply these reflections to flip across an edge or vertex of the yellow face, rotate about the centre of the yellow face (e.g. s_0 s_1), and transpose the yellow face with any other face

In this manner we can represent every symmetry of the barycentric subdivision, and by extension, the tetrahedron, in terms of these three reflections. If you don't see this, consider the effect of conjugation.

The sphere is a surface of constant curvature

This tiling generated by the tetrahedron is a regular tiling of the sphere

In short, the tetrahedron has a symmetry group S_4 (often called A_4 in analogy with the Dynkin Diagram) that has a presentation in terms of three reflections, which act transitively on this barycentric subdivision. The angles of the barycentric subdivision correspond to the relations of the presentation. One can generalise this observation and use it to classify polyhedra.

Some theoretical results.

A Coxeter group is a group W accompanied by a set of generators S = {s_1, s_2, ..., s_n} \subseteq W, such that W = <s_i | (s_is_j)^m(i,j) = 1>, where m(i,j) is an integer at least 1, m(i,i) = 1, and m(i,j) > 1 if i != j. These relations turn out to exactly correspond to the relations necessary to define a finite system of reflections in (n+1)-dimensional space.

By polytope, I mean a bounded convex polytope.

The regular tilings of the sphere correspond to regular polytopes, which correspond to the finite irreducible Coxeter groups whose Dynkin diagrams have straight lines

We can define a polytope to be regular if the automorphism group of the polytope acts transitively on the regions of the barycentric subdivision (or equivalently, its "flags"), which corresponds to chains of i-faces of the polytope ordered by inclusion

To go from a polytope to its Coxeter group, you take its automorphism group to get the group structure, and do a similar thing to above to find the generators, you arrange some hyperplanes so that their reflections satisfy the relations of the Coxeter group, generate a system of hyperplanes closed under reflection, and intersect this with an (n-1)-sphere to get the barycentric subdivision, from which you can recover a polytope and its dual polytope, which have isomorphic Coxeter groups

The regular tilings of the plane correspond to the affine irreducible Coxeter groups with straight line Dynkin diagrams.

One can study the regular tilings of hyperbolic space and classify those Coxeter groups too.

The E_8 lattice, which gives solution to 8-dimensional sphere packing has a a load of other interesting properties, corresponds to the Coxeter group E_8, via a certain semiregular polytope which is the convex hull of some lattice points.

The classification of regular (n-dimensional) polytopes and regular tilings of R^n is via the classification of Coxeter groups (and by extension Dynkin diagrams with certain properties)

There is an elegant classification according to Bourbaki that resembles the typical intuitive classification of regular polyhedra and regular tilings of R^2

Fun extensions

There are a lot of ways to represent a symmetry of a polytope/element of a Coxeter group in terms of the reflections/generators s_i. Is there an easy way to determine whether your representation of the symmetry/group element is the shortest? Yes! In fact, you can construct a DFA on the generators in the finite case.

The Cayley graph of a Coxeter group is Hamiltonian

My pfp shows the duality between an octahedron and a cube. If you draw a vertex at the centre of each face of the cube, and take the convex hull of the vertices, you get an octahedron. Note that vertices of the octahedron correspond to faces of the cube, edges of the octahedron correspond to edges of the cube, and faces of the octahedron correspond to vertices of the cube. Two vertices of the octahedron are incident with each other when the corresponding faces of the cube share an edge, and so on. To put it formally, the poset of i-faces of the octahedron and the poset of i-faces of the cube, both under inclusion, have an anti-isomorphism between them. This causes them to have isomorphic symmetry groups.

The cube has its Coxeter group with relations (s_0s_1)^4 = (s_1s_2)^3 = (s_0s_2)^2 = s_i^2 = 1. Note that here the 4 and 3 are different numbers, and the cube has a dual of an octahedron. In the case of the tetrahedron, the exponents are the same, and the tetrahedron is self dual. In general, finite irreducible Coxeter groups with straight line Dynkin diagrams correspond to self dual polytopes exactly when their Dynkin diagrams are "reversible".

This is heavily related to how the cube and octahedron have reversed Schl\"afli symbols.

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 3

Propaganda

Cube:

Also called the Regular Hexahedron

Platonic Solid

Regular

Dual of the Regular Octahedron

It has 6 square faces, 12 edges, and 8 vertices.

Oh, cmon! The cube is great! It tiles space, its one of the platonic solids that has analouges in all dimensionalities, its vertices are can be mapped to the strings of three binary digits in a structurepreserving way, and its literally the most iconic shape of all time!

Image Credit: Tumblr

Rhombicuboctahedron:

Also called the Small Rhombicuboctahedron

Archimedean Solid

Semiregular

Dual of the Deltoidal Icositetrahedron

It has 18 square faces, 8 regular triangular faces, 48 edges, and 24 vertices.

Image Credit: @anonymous-leemur

Truncated Icosidodecahedron:

Also called the Rhombitruncated Icosidodecahedron, Great Rhombicosidodecahedron, Omnitruncated Dodecahedron, Omnituncated Icosahedron

Archimedean Solid

Semiregular

Dual of the Disdyakis Triacontahedron

It has 12 regular decagonal faces, 20 regular hexagonal faces, 30 square faces, 180 edges, and 120 vertices.

It has the most edges and vertices of all platonic and archimedean solids.

Of the vertex-transitive polyhedra, it fills up the most of the volume of the sphere it fits in (89.80%).

It is not actually the shape you get when you truncate an icosidodecahedron, although it is topologically equivalent.

It is the mod's favorite three-dimensional shape.

Image Credit: @anonymous-leemur

[map-projection-showdown]

WATERMAN BUTTERFLY vs ORTELIUS OVAL

Waterman Butterfly Polyhedral Compromise

Designed by Steve Waterman in 1996, the Waterman Butterfly projects the globe onto a truncated octahedron, which is unfolded into a "butterfly" shape inspired by Cahill's 1909 projection. The specific octahedron used is based off the convex hull of packed spheres, which is what Waterman was originally working on when he created this projection. Usually presented with Antarctica in a separate circle below the map, see below the cut for this.

It is one of the projections featured in xkcd 977.

Ortelius Oval Miscellaneous Compromise

First created by either Battista Agnese in 1540 or Abraham Ortelius in 1570, (Unknown if Agnese's map is the same construction), this map was used for the world map in what is considered the first modern atlas, the Ortelius' Theatrum Orbis Terrarum. It was widely used for world maps during the 16th and 17th centuries, but has since fallen out of use. The front hemisphere forms a circle that is the same as the Apian I projection.

[link to all polls]

Waterman with separate Antarctica:

Political:

Tissot's Indicatrices:

Images created by Tobias Jung (CC BY-SA 4.0) from map-projections.net

[bjfinn]

Beetlejuice headcanon #4:

There's another connection between Beetlejuice and Lovecraft: non-Euclidean geometry.

From Atlas Games (7 July 2016):

"The Maddening Architecture of R’lyeh"

H. P. Lovecraft’s descriptions of the sunken city of R’lyeh in "The Call of Cthulhu" focus on its unimaginable, mind-bending appearance. It’s easy to imagine slimy green, algae-covered edifices that have sat at the bottom of the Pacific Ocean for untold eons, but what about those more obscure terms and concepts?

In the story, Henry Anthony Wilcox describe "great Cyclopean cities of titan blocks and sky-flung monoliths." This refers to the style of ancient Greek architecture of Mycenae, which stacked stone blocks tightly together, without any mortar. And monoliths are no more than slabs of stone, like those found at Stonehenge.

Later in the story, the crew of the ship Emma actually lands on and explores the risen island which they find off the coast of New Zealand. Their descriptions suggest something more madness-inducing: "He had said that the geometry of the dream-place he saw was abnormal, non-Euclidean, and loathsomely redolent of spheres and dimensions apart from ours." They say that the walls appeared both convex and concave at the same time. Imagine walls that looked like both versions of that building at the same time. It would certainly give a viewer quite the headache, if not a case of psychosis.

The above photo is of one of the cards in the game "Lost in R'lyeh" (Atlas Games: illustrated by Kelley Hensing) -- it certainly looks a lot like the architecture of the Netherworld, and when Beetlejuice and Lydia take over the house the architecture shifts to the same non-Euclidean geometry.

Even when they draw the door to the Netherworld, it has the same skewed nature -- that's not sloppiness, that's the inevitable effect of creating a doorway to another plane of existence.

[rhodesmusic]

The boundary of a tricylinder is a rhombic dodecahedron: graphing polyhedra with implicits and expressing them as Minkowski sums

The day before yesterday (or rather, yesterday at 12 in the morning) I was mathing on discord and a friend brought up Steinmetz solids, which are funny shapes obtained by taking the intersection of two or three cylinders. As the cylinders pass through each other, they outline a shape where they cross, which is the Steinmetz solid. Taking two cylinders gives you something called a bicylinder, and similarly, taking three cylinders gives you something called a tricylinder:

Images from Wikipedia

They showed me this and I was interested in the diamond-like pattern of the corners and edges on the tricylinder. Looking at it, we can see that the points at which all three cylinders intersect form a cube, and the other corner points come from where two cylinders intersect in the middle of the third, which seem to be positioned in the middle of the squares from the cube. Plotting this out and projecting the vertices onto a sphere to get a better idea of how they're arranged, I got this funny shape, which is called a rhombic dodecahedron, apparently:

Made with desmodder for desmos graphing calculator, graph link

I guess the name comes from how all its faces are rhombuses and how it has twelve faces, the same number of faces as a dodecahedron. Sharing this with them, another friend's immediate reaction was "oh SHIT it's the"

along with this implicit plot of the rhombic dodecahedron in a 3-d grapher (a really cool one, by the way) (also, not the exact image they sent, just recreated it lol). What immediately caught my attention was how simple this implicit equation was. It seemed awfully convenient how this complex shape could be described so concisely with an implicit. I looked up the rhombic dodecahedron on Wikipedia, and found that it was, in particular, a zonohedra, which is a competitor for the most fuckin silly math term of all time.

A zonohedra is a convex polyhedron which is centrally symmetric, possessing a special kind of symmetry, but what's sick is that a zonohedra may be equivalently described as a Minkowski sum of a collection of line segments. A Minkowski sum of two shapes is just the shape you get when you take any point from the first and add it to any point in the second, via vector addition. You can repeat this to get the Minkowski sum of any number of shapes in any number of dimensions, and when the shapes are all line segments, you get a zonotope (lmao).

Thus, 3-dimensional zonotopes are these zonohedra, which come from taking some number of line segments in 3 dimensions, and then going through all combinations of points on them, picking one point for each segment, and adding them together. The rhombic dodecahedron turns out to be the Minkowski sum of the line segments forming the long diagonals of a cube, and I can't help but feel like the simplicity of it's implicit equation comes from how it can be expressed as a zonohedron.

(Me realizing the rhombic dodecahedron is a zonohedron)

Thus, I'm interested in how you could get from a zonohedron to a Minkowski sum, and then to an implicit plot, or maybe the other way around from an implicit plot to a Minkowski sum (though this requires you know the implicit gives a Minkowski sum to begin with). For example, any cube is the Minkowski sum of three orthogonal line segments of equal length (letting the lengths vary gives you a cuboid), and the unit cube has the implicit equation

max(abs(x),abs(y),abs(z))=1,

so I wonder how you could derive the implicit from the Minkowski sum. (Unfortunately, the cube is the only Platonic solid that's also a zonohedra, since it turns out that the faces of a zonohedron have to have an even number of sides, so womp womp for expressing the tetrahedron, octahedron, icosahedron, or dodecahedron as Minkowski sums of line segments.)

Note how it doesn't matter if you translate a shape in any direction when taking the Minkowski sum, since the resulting shape will be congruent to to what it'd be without translating, namely, it'll just be that shape translated in the same way the component shape was. This means you can translate the line segments in a zonohedron's corresponding Minkowski sum so they all sit at the origin, so that every one of them can be described with the vector sitting at the end of the line segment; the zonohedron can be derived from just a collection of vectors. This site I found gives these vectors for lots of different zonohedra.

So, given some 3-dimensional vectors, how would you get an implicit equation plotting the zonohedron they represent? I'm working on this for the 2-dimensional case, with the goal of being able to bump it up to 3-d or even generalize it to n-dimensions once I figure it out.

Also, another thing I'm mildly curious about. In my opinion, the tricylinder is much more cool and swag than the bicylinder because the 3 cylinders it comes from make full use of 3-dimensional space and thus we get a cool polyhedron from it (the bicylinder gives you something called a hosohedron). An infinite (filled-in) cylinder can be thought of as the Cartesian product of a disc with the real line, for example, for an infinite cylinder around some axis, you take a disc orthogonal to that axis and sweep it back and forth along the axis.

This proposes a generalization of the tricylinder: In n-dimensional space, take n copies of the Cartesian product of an (n-1)-ball with a line. Namely, for each axis from the canonical basis, take the unit (n-1)-ball sitting orthogonal to that axis and sweep it back and forth, getting a (filled-in) "hypercylinder" (don't know if this is the actual name for this). If we take the intersection of these hypercylinders, what's the n-dimensional polytope we get from the boundary of the intersection, that is, the graph we get from the boundary? (How to even define this boundary graph, that is, define what the vertices and edges are in a way that generalizes to n-dimensions is the first step).

For 2-dimensions, the 1-ball is just a closed interval, and the cylinders are just infinite strips, so the intersection is the filled-in unit square and the boundary is a square. The boundary of the Minkowski sum of 4 line segments, starting at the center of a square and ending at its vertices, is also a square. Similarly, for 3-dimensions as we saw we get a rombic dodecahedron, which is equivalent (as a graph) to the boundary of the Minkowski sum of 8 line segments going from the center of a cube to its vertices.

If this pattern continues, which I feel like it should, it'd give an equivalence for this question, namely, the n-polytope coming from the boundary of the intersection would be equivalent (graph-isomorphic) to the n-polytope coming from the boundary of the Minkowski sum of 2^n line segments, going to the vertices of the n-hypercube. (Note that we could just take 2^(n-1) line segments going to just the vertices of the top half of the hypercube to get an equivalent shape up to some translation and dilation, this is what the website I linked five paragraphs ago does.)

That's all for now. Will post an update on this if I find somethin!

[alyss-erulisse]

Burger On The Grill

Part 18: Setting the Table--French Fries

After completing the donut tutorial by Blender Guru, I was challenged to create something similar by myself, so I made a burger. I will make that burger into a meal with a soda and fries.

In the last part, I set up the scene with a burger and soda. Now, I'll add in a pile of fries.

Build Some Fries

For issues of scale, start with a bit of research.

The official julienne size is 1/8 inch × 1/8 inch × 2 inches. The next thicker cut, batonnet, is 1/4 inch x 1/4 inch x 2½ to 3 inches. The baton is the thickest stick cut: 1/2 inch x 1/2 inch x 2-1/2 inches.

I chose a fry thickness of 3/8 inch x 3/8 inch. The length will vary between 2 and 3 inches. A thicker fry will deform less, which simplifies our physics. Fries can be bendy and their edges can be tampered like the round edge of a potato. Their edges are not perfectly sharp.

Find a reference image. Choose several fries in the image that you like the shape of. Start from a cube primitive and model 3 french fries of different sizes and shapes.

Add a material to your fries. Add Noise Textures of difference scales together and use them to drive the Base Color and Displacement. Pick light colors from the reference image for the Base Color range, and choose a 0.0008 scale for the Displacement.

Add Subsurface Scattering of scale 0.125 with Subsurface Radius (0.3, 1.8, 3.8) and Subsurface Color a saturated gold. Increase Roughness to 0.761 and Transmission to 0.468.

See Fried Potato Material Nodes image at the top of the post.

To see the full effect of the Displacement, add a Subdivision Surface Modifier to your french fries. Set it to Catmull-Clark, check Adaptive Subdivision, set the Dicing Scale to 1 and the Levels Viewport to 5 with Optimal Display.

Prepare for Placement

Creating a stack of french fries by hand is a lot like trying to manicure your lawn with a pair of kid scissors, a painful waste of time, especially since the advent of lawnmowers and rigid body physics.

Do yourself a favor. Save the manual placement for relish.

Of course, using rigid body physics correctly takes a little planning.

We want a fast working environment, so replace dense meshes like the soda and the burger with low poly objects that can act as placeholders.

To prevent fries from passing through the placeholders, add Rigid Body to these placeholders with these settings: Type: Passive; Shape: Convex Hull.

To prevent the fries from floating above the serving paper instead of resting on it, add Rigid Body to the serving paper with these settings: Type: Passive; Shape: Convex Hull; Margin: 0.0001m.

Add Rigid Body to one french fry with these settings: Type: Active; Mass: 0.3kg; Shape: Convex Hull. Use Copy from Active to duplicate these rigid body settings to the rest of the french fries.

Now, if you just drop the fries like we did with the ice cubes, you'll end up with this sparse madness:

Instead of just dropping them on a flat surface, imagine how they are placed on the plate in real life.

Watch some videos of restaurants making fries. At McDonald's, fries start out in a basket which is dipped in oil. They are poured into a bin, scooped out and then funneled into a container.

Falling Fries by CG Artist Academy

In the tutorial above, an angled plane funnels to a drop. The fries slide along this angled plane into a bowl.

From here, we can rotate the bowl so that the pile of fries then slides onto the sheet of paper like in this image.

Begin by modeling the funnel and the bowl. You won't see these objects in the final render, so they don't need to be fancy. A few adjustments to a cube and UV sphere will get you something usable.

Add Solidify Modifiers to make sure your objects are nice and solid. We don't want our fries to get confused and fall through them like ghosts passing through a wall.

Create duplicates of your fries and place them over the funnel. Add Rigid Body to the Funnel and the Bowl with these settings: Type: Passive; Shape: Mesh; Margin: 0.005m.

Here is what the simulation looks like so far.

You can Apply Transformation to that group of fries once it is settled. Then, if you need more, you can send a second group down the shoot into the bowl.

Serve the Fries

Under the Rigid Body settings of the bowl, check animated. Now, when the bowl is moved, the fries will follow.

Create a keyframe at frame 1 for the initial position and rotation of the bowl. Now, imagine you are pouring the fries onto the paper. How would you move the bowl?

Create more keyframes for the movement of the bowl. See how the fries fall onto the paper.

I created some perimeters to contain the fries on the serving paper with Rigid Body settings: Type: Passive; Shape: Mesh; Margin: 0.001m.

There was a lot of tweaking as I changed the animation to get the fries to stack and flow the way that I wanted. I concentrated on trying to get the congregate shape to look good inside the picture frame.

Once you have something you like, Apply Transformation to the fries.

Clean up the materials list by selecting all of the french fries. Set the material of the active object to the french fry material we created. Then, click the downward pointing arrow to the right and select Copy Material to Selected. Now, all the fries should be using the same material and not a duplicate.

Finally, we have all the elements we need in our scene.

Follow me to keep watch for the next part! We'll be adding the finishing touches to our scene with some background textures, color grading, stage lighting and camera effects.

Review the previous part.

See overview for links to all parts of this tutorial series!

See more of my work: Check out my archive.

Join me on my journey: Follow me on tumblr.

Support my creative profession: Buy me a coffee on KoFi.