#sierpinski carpet

[rlyehtaxidermist]

You're actually making a good point, I'll give it some thought. Thank you.

Although I was being generally nihilistic about the concept of having a discussion in the first place, when you're an insane freak with fringe ideas, the only thing you can do is petty acts of malice and plotting the demise of the human race if you're in a good headspace. I wrote what I did because I liked your blog, but I was so disappointed to see you supporting mainstream ideas about morality. What is your favorite fractal?😔

Aesthetically, the Burning Ship.

In general, Cantor's ternary set and its close relatives are too useful as counterexamples to not take the top spot.

[rockatanskette]

You know what? Fuck it.

Girl Dinner

Carme Ruscalleda i Serra, who holds seven Michelin stars across her three restaurants in Catalonia and Japan, known for bringing traditional Catalan cuisine to an international audience.

Mashama Bailey, winner of the 2022 James Beard Award for Outstanding Chef and Chairwoman of the Edna Lewis Foundation, which preserves and celebrates the history of African-American cookery.

Zineb "Zizi" Hattab, the first vegan chef in Switzerland to be awarded a Michelin star for her restaurant KLE in Zurich; her cooking is noted for its intense flavors and complex balanced dishes in a casual setup.

Girl Math

Maryam Mirzakhani, who won the Fields Medal (the most prestigious award in mathematics) in 2014 for her work on the dynamics and geometry of Riemann surfaces.

Hee Oh, Vice President of the American Mathematical Society, who has worked extensively on counting and equidistribution for Apollonian circle packings, Sierpinski carpets and Schottky dances.

Svetlana Jitomirskaya, who co-solved the Ten Martini Problem in 2019 and won the Dannie Heineman Prize for Mathematical Physics in 2020.

Girl Economics

Esther Duflo, co-founder of the Abdul Latif Jameel Poverty Action Lab at MIT, professor of Poverty Alleviation and Development Economics, and co-recipient of the 2019 Nobel Memorial Prize in Economic Sciences.

Mariana Mazzucato, chair of the World Health Organization's Council on the Economics of Health for All and member of the United Nations' High-Level Advisory Board on Economic and Social Affairs.

Gita Gopinath, deputy managing director of the International Monetary Fund, awarded the Pravasi Bharatiya Samman award in 2019 for her work as an economics academic.

Girls* are fucking rad actually. Pay them the respect they're due.

*This statement enthusiastically includes trans girls and women. Bigots kindly fuck off.

[mathysphere]

My mom does a lot of very involved cross stitch projects that take a long time (she recently finished a pattern made from a photo of Denali that took a year and a half) BUT the project she just started is a Sierpinski carpet on a tote bag, planned out as 2^9 9x9 squares, which I thought y’all might appreciate.

Omg that's incredible! That's a dream project right there-- I've daydreamed about making a Sierpinski carpet cross-stitch before, but the sheer repetition of even a medium-sized one intimidates me.

Tell your mom she's a legend! With good taste! That kind of year-long piece is just incredible.

[msexcelfractal]

You can generate Sierpinski carpet (the 2D analog of Menger sponge) at home! I started with addition modulo 3 and some conditional formatting in Excel.

I left the modulus configurable. Powers of 2 produce simple tessellations instead of fractals, so the first viable fractal is A1=3. Here's the modulus 3 image at 729x729 resolution:

This is the standard sierpinski carpet. But starting with modulus 5, higher primes are going to give us some trippy Menger-analogs with intricate self-similar geometry. Let's dive in:

Modulus 5

Modulus 7

Not all composite numbers are duds! Mod 9 is beautiful with its single order 3 subgroup.

But Mod 15 is not so much a fractal as a self-similar glitch. The subgroups of order 3 and 5 are all jumbled together!

Modulus 17

Modulus 19

Modulus 23

Modulus 29 with 707281 cells. (That's 29 to the fourth power!) And that's the limit, because Excel is running garbage collection nonstop trying to compute any more of the image. Excel 2010 was limited to 2GB of ram and we are out. I call this collection of renders "seafloor".

[jonathankatwhatever]

It is 8 Mar 2023. Since time is short, let’s get to work. I ran into an interesting problem, which is the concept behind injective, surjective, and bijective. These are all mappings, which immediately says I//I to me because that is how these maps can both exist and map, with the mapping being within the DR framework. And each mapping has to be over a Counter, which generates Observer, which now fits to the model as the D5 enabled space in which the D4 enclosures, grid squares and boxes and the like, permute and otherwise order so we get the worlds we see and imagine. That is now provable.

Let’s try an application. A space-filling curve has to self-intersect without crossing, so attaching as an edge, which we describe as being 1Space consists of Ends to which 1-0Segments Attach. This enables connection into the End, which also has other connections, so we can say the Attachment doesn’t intersect in the sense of crossing the counter in that End, meaning over a division, over a count. That is why the self-intersection adds the cut-points which are inherent in a line segment. I hope I don’t have that entirely backwards. Let’s see. So, in the one case, the intersection has to be ‘reduced’ to End, meaning we take out the area, volume, etc. which projects when we actually intersect. And I’d bet in the other the intersection inherent in the End that is a cut-point is ignored, meaning we ignore the area, volume, etc. inherent in that being an intersection. Combining these two means a method of focus. What did I just say? A method of focus in which I//I operates. Don’t get that either, but keep going. I//I operates off ideal Irreducibles, which you approach through the process by which an End becomes an intersection because that is where the Bip is the best or clearest defined. Okay. I got that. I assume that means factored process structures, meaning polynomials, meaning this could be considered as a training function of AI on a bimodal distribution, which again shifts us right into elliptics and poles and holes.

The Peano curve uses a form that generates, in essence, the point outlines of gs(n) and gs(m). I can see why: as Ends, they have boundaries, so you can squash them together as the space fills but this curve, this process fills all the space around the process, around the space being filled, which is easy to see in projection to a square covered in a grid of tiny grid squares in both forms. They are projections of layers, not a single layer, which you can see in the description of the curve itself.

So we can say that a line segment and a square have the same cardinality, and that this relationship is clearly surjective because it generates both Irreducibles. Peano actually used or uses SBE3 and flips the grid squares 1-0-1. I’m sure we covered this before, but you can literally see the gs(n) with the curve connecting gs(m). The relationship is obviously not injective and not bijective.

Hilbert reduced to IC. And that introduces a lot of flipping. I see that Lebesgue draws N’s, meaning a scaling diagonals. Flip that and you get S and Z. Invert and get M. I can now see a number of gesturals.

And Sierpinski combined triangles and grid squares. You can really see this in the way the similarities flip even and odd, with the even looking Hilbert-like. These are all ways of filling space using I//I.

————

I see a Sierpinski triangle is fT. Take out the center, which is I//I, and keep iterating within each, thus progressively growing one Triangular sheet whilst removing the Irreducible.

That was fun! Took like a second to get.

Sierpinski carpet removes a square from SBE3. This means it recursively generates CM64 through the scales by locating the center square in the other Irreducible. That is what enables CM100 over I//I. Wow.

So, a Sierpinski curve has a ton of permutations, most which only go so far before failing, meaning they reach their calculation limit or whatever it is when the permutations, when the flips required to keep going above become too difficult to calculate, which is another example of surreals versus reals.

This is massive proof. The words keep coming but I can’t get them down. This proves the inherent ordering to the pole by mapping not merely values but process from unit segment to unit square. This is 1-0Segment to grid square. We see the Irreducibles in the ‘carpet’ constructions, which are of course fractal, and we see in the curves constructions the permutations across IC derived combinations that literally connect this to this in an ideal manner so the various pieces, when flipped and rotated as necessary, in the inversion processes described, form a map and act as a mapping function of a grid square. Note that these are all derived from looking inside a grid square, which is appropriate.

Now, again, you see constructions like CM28 take shape: if you have 7 of these as connectors, then the placement of the 8th determines a fit to the half, so if you both connect over that then you compress the count by 4 to 60, which allows other attachment choices. Note that Attachment with a capital A includes a flip potential. As in, there’s a 4square piece and it’s oriented this way, which would fit to this other structure if it’s oriented that way. Both evaluate. And that’s an example of the extra process inherent in one path, and thus why we trade efficiencies for quality in both directions.

———

Trying to keep this going because I feel this is an extraordinarily deep proof. I’m seeing the glyphs, meaning the ways you can draw a 4square in Hilbert form, all being available and flipping to the states necessary to generate specific results. So CM28 isn’t a fixed point but a fixed inflection, meaning a choice is made at CM32 because that mirrors to CM64, meaning that if you take out the center square from SBE3, you have one empty one at 7. What about 36-28-36, a woman’s figure perhaps? If these are connections to the neighboring layers, then that 6 could also be 24, which makes me think D24 or 4SBE2. That would require a shift in counting with the layer, so the count at these layers is the count of squares that are 4squares, which of course is true about all grid squares counts. So that actually works perfectly.

Viewed as automorphisms, this makes a lot of sense. And these generate that surjection from the grid square to the 1-0Segment. I can see the utility in the words, but I think to me injection means less than or equal and surjection means more than or equal and bijection means both of those are equal.

It would be neat to connect the Peano curve to b10 through attachment. That would in the Ends or Attachments of the snake, which occurs in one of the glyph forms, of which there must be 4 basic ones, so we have redone the idea that b10 is a continuous progression which links SBE3 structures together. Where is that 1? It’s in the 0 at either End of the snake, which puts it into the action of dividing each of the squares into SBE3 again and again and again, with b10 fitting the pieces together. That is a truly beautiful result!

I remember we did this before, but it wasn’t as complete. Nice to see all those weird and sometimes wild conclusions were true. Even glyphs and the orientations of reading across the grid.

————-

Just this moment realized this demonstrates I//I over the layers as the operation in CM100, that it combines layers (of layers, etc.) through the I//I process which you can think of in various ways, including the ones discussed above. Another is as torsion points or I assume sets, meaning the central End in an HG or Hexagon or the 3rd End in Triangular. And in other cases, the 4th point which can’t be specified rationally when any combination of the 3 can. Why is that so? I know it’s the Bip, so the combinations move around the pole. That connects to the discussion yesterday about elliptics and defining the hole as the pole.

That’s an interesting sexual idea.

——————

So, we’ve proven that I//I exists, and that gs(n) and gs(m) layers exist. Using stuff that dates back to the 19thC, and putting that together with extremely modern ideas like surreals, which date back to the mid-1970’s, and model theory and the like, which is really newer than that. A real feat of sK associativity and zK counting. The highest z-score I’ve ever seen means sK can associate far enough to see these ideas, and to see them with increasing clarity. We make quite a team.

Don’t you love this material? We can explain it in great depth, and can attach all the processes necessary to show how that depth works. I note a particular favorite is the return of the 9 to 10 counting. That’s a subject we worked out when f&b came up, that a field of these flipped SBE3’s are counting that (1+(SBE3)+1) glyph in which the 10 count links the 9’s over a surface that has lots of local inversions within any state, and which has ideals which maximize (or minimize or balance, etc.) the scope of inversion. Layer after layer of process.

Weird thought: can we attach this to a conception of time or Conformal Reality or, even better, Tractable Reality? I can see all the above, with the first being the Counter processing at a constant rate connected to the IL. Conformal and Tractable Reality are structure related, meaning the conception of local is that which is tractable within the conformal requirements of time. That’s not bad. It will get better. Example: a method is for CM100 to generate a high level this side, like all the issues within an election, and how those then play out. That occurs because that is Tractable. Conformal is about the forces which generate the choices, which generates the issues in focus, so Tractable Reality is that which either reduces to what we actually get (and which creates the gaps between ideals and visions and hopes, etc.). That is really cool material!

—————

I realized this explains a lot of the weirdness I see in ‘arguments’ made. Some are obvious, like I read a piece in which a Palestinian argues, in effect, that because there are 2 routes to the same conclusion, the arguments are actually fundamentally different. He says the 2 state solution has failed, so the 1 state solution is the choice, meaning that refusal to agree means the other side now has to agree. This is taken as logical by vast numbers of people. The other is that I read the Justice Department’s criticism of the Louisville PD and I could see how the sides problem arises: impose a solution on the police without looking at their perspective sufficiently, without thinking about how to address those issues but instead requiring one side in a relationship to change, and that leads to failure. This stuck out because a large part of the report is about how the police objectified people, treating them as criminals or as problems rather than as humans and humans with challenges. So we identify this relationship, which has to be a surjection, and then impose a solution as though there were a bijection. That is already proven math, applied through grid squares to ordinary life.

This stuff actually works!

[is-this-plural]

we're personally fond of the sierpinski carpet

the Mandelbrot Fractal (beloved)

FRACTALS MENTIONS 💯💯💯💯💯 WOOOO FRACTALS ‼️‼️‼️‼️‼️‼️ NO. ONE FRACTALS FAN 🔥🔥🔥🔥🔥🔥🔥yeah plural

[crazyskirtlady]

~Adjust perceptions~

s h i f t s h i f t

[isomorphismes]

ℂ→ℂ

[tunastudy]

Fourth-iteration Sierpinski Carpet

a doodle by moi (don’t worry, this was on graph paper, I’m not superhuman)

[z-arcane]

Sierpinski carpet addition

RENDERING FRACTALS

Written in Python using numpy, pyplot, and numba for the jit compiler.

[thespamman24]

THINGS THAT ARE FORBIDDEN IN MY NEW RELIGION:

1.Saying mean things to children

2.Giving dogs the name “Wet Beef”

3.Vacuuming your front yard

4.Giving cats the name “Dry Beef”

5.Tattooing the name of all your body parts onto yourself

6.Discussing the Coastline Paradox

7. Giving yourself tattoos at all. That’s very dangerous.

8.Naming your right elbow “Beef”, then tattooing the word “beef” on that elbow

9. Naming your left elbow “bell pepper” then tattooing the word “bell pepper” on that elbow

10. Having a ridiculously small tongue.

11. Forcing a four legged creature to dance.

12. Messing up a crime scene by pouring salt and butter all over it

13. Messing up a child by pouring salt and butter all over them

14. Marrying one of your elbows. The other one will get jealous. Marrying both of your elbows is fine, but divorce is not recommended because then you won’t be able to use your arms well.

15. Pretending that a lizard is something other than a lizard (a kangaroo, a rock, another kangaroo)

16. Challenging an alternate version of yourself to a boxing match, and then falling in love with your alternate self. This will destroy the universe.

17. Calculating the exact geometric configurations of Gabriels Horn

18. Giving trees the power to smell things. This will make them too powerful. They will then be able to smell each other, all in love, and marry. And, when the trees go on their honeymoons, their will be no one left to give us any oxygen.

19. Any discussion or conversation of other concepts related to fractal geometry including (but not limited to), Sierpinskis Traingle, the Koch Snowflake, the Picard Horn, the Pseudosphere, the shape of the universe, The Mandelbrot Set, self-similiarity, non-differential functions, measure theory, infinite recursion, the Hausdorff-Besicovitch Demension, a Julia Set, the Sierpinski Carpet, a finite subdivision rule, and the Topological Dimension.

20. Naming your children “Bell Peppers and Beef”

[epikulupu]

[ ⭘ ] ​ SIERPICARPETAN ! ╰┈➤ ​ ​ a gender related to the sierpinski carpet fractal. ╰┈➤ ​ ​ sier + pi + car + pet + an ╰┈➤ ​ ​ from 'sierpinski' and 'carpet', and the suffix 'en'. ╰┈➤ ​ ​ requested by no one, coined by us. ​ [ ⭘ ]

[spankymerve]

A Sierpeniski carpet, if you will

sends you a pixelated dick pic

[altsoph]

In Scotland, there is such a phenomenon as tartans. These are textile patterns, unique for districts, clans, families, etc. (examples in Fig.A); historically, they play a role similar to the coat of arms; they are used to create kilts, scarves, etc. The first tartan found, Falkirk, dates back to ~250 AD, and now there are a lot of them — more than 3000 are currently registered in the official register.

They look pretty different but could be simply parameterized by generator codes like G106R26B4Y44 or G24K8G2K8, so it's easy to generate them, and there is already a twitter bot alltartans for it (Fig.C). On the other hand, these patterns are similar to unfinished fractals, so there are attempts to draw hyperbolic tartans (Fig. C). The square of the Cantor set is also called Cantor Tartan (and is similar to the Sierpinski carpet, Fig.D); for some reason, someone is trying to define a calculus on it.

Also, while writing this post, I discovered a strange carpet sect, Triangle Frenzy.

[mathhombre]

Sierpinski Carpet

A doodle for Sophia Wood’s #mathober, with four generations, on the theme of iterate. See all the themes here.

[nonbinary-octopus]

okay so I got the Bundle for Racial Equality and Justice at itch.io and I’m looking through all the games in it.

There’s one called “crashed lander” that looks pretty fun, and I’d already decided I was gonna play it when suddenly the video showed a level with 3D Sierpinski Carpets, which made me even more interested in playing it.