#Fractals

[rbrooksdesign]

"DMT-EDMT Series for December Geometry #21"

From another perspective...

Yesterday's post(s) (#1-20)

The Butterfly Fractal 1 (BF1) is a fractal resulting from the simple doubling of quantity "1" -- 1 -- 1x2=2 -- 1x2x2=4. -- 1x2x2x2=8, -- 1x2x2x2x2=16

When you lay it out into its "Butterfly-like" array, you can see that every "1" becomes a new source for the self-similar, re-iterative redundancy of the same "fractal" pattern within.

The BF1 pattern is repeated on both sides (of the "wings.”)

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Today...

The BF1 expands to reveal the 4th "container" in the series: PN6-->PN28-->PN120-->PN496 with PN496 -- like the other two in BOLD -- being a TRUE Mp-PN pairing.

Notice how all four are within the butterfly image. PN496 with x=16 starts at the p=5th level up, with 16 RED "1s" across. Each "1" is the start of a new BF1 fractal going up 1--2--4--8--16.

The Running Sum (∑) 31 is shown at the top of each BF1 sequence. 16•31=xz=PN=496.

As the butterfly expands, both the graphic and numerical representation of the fractal quantity expands so fast that soon it becomes very difficult -- like trying to see individual stars when gazing at the larger Universe -- that we are forced to look at it summarily. The next four TRUE PNs are 8128 -- 33550336 -- 8589869056. Yet, in every case, they follow this same BF1 template! Only the numerical values increase as the template grows, AND, the history of the previous "containers" is always present within. This is true entanglement!

For those keeping track: the Mersenne Prime (Mp=z) "containers" are also historically present within the template as it grows. They are the ∑s: 1+2=3, 3+4=7. 7+8=15 and 15+16=31.

And, of course, Mp² = z² = Mersenne Prime Square (MPS) = xz +yz = PN + OC.

[todays-xkcd]

I'm sure the building inspectors will approve my design once they finally manage to escape.

Log Cabin [Explained]

Transcript Under the Cut

[The floorplan of a log cabin, with a fullsize layout on the left, while on the right is a sequence of increasingly smaller versions of the same layout, like a golden rectangle.]

[Caption below the panel]: Log cabin

[mrvelocipede]

polychroma.bigcartel.com

polychroma.threadless.com

[rayetherna]

And this, my friends, is a fractal horse, which was inspired by a glitch in a 3D model of a friend’s horse OC XDD The portrait “sprouted” multiple snouts and I just had to take the idea and run off with it to “brew” more monsters.

[thesorceresstemple]

1 : "Never ending Cosmos" / F.W.Stumpfi 1979 2 : "Split" / F.W.Stumpfi 1979 3 : "Infected by Chaos" / F.W.Stumpfi 1988

[chasingrainbowsforever]

~ Blue and Gold ~

[mycrystalearth]

🐚 ammonite fossils 🐚

[kereonn]

Crowned☆

©Kereonn Xxx

[ovytia-art]

Fractals was a bit of a challenging prompt for me. My first association with ‘fractals’ is the fibonacci sequence and endless spirals, and you know what that made me think of? The infinite realms.

Hard surfaces are hard for me, so yay for cel shading

DannyMay Masterlist

[blake447]

So in case anyone's following and seen my work with dragon and koch curves, and was curious about sierpinski's triangle, it can be represented with these sequences but unfortunately the process is more irregular so we cant pull the same tricks with binary sequences, at least in any manner that is immediately obvious.

Pictured above is a process where you double each element of the sequence, and pick a number to inject smaller triangles into, then repeat the process. With a bit of practice you can draw an eularian path that forms a sierpinski triangle.

If you wanna get really fancy you can vary the edge you break into smaller triangles each iteration, though its really, really hard to do on the fly

This is one i've always wanted to write a program to generate.

[rbrooksdesign]

"DMT-EDMT Series for December Geometry #20"

acrylic, 25"x40", 2024, Reginald Brooks

[lesbianslovebts]

For this project, I took a stage 9 dragon curve and implemented the following rule: for each of the stage 8 fractals contained within the stage 9 fractal, where 4 lines enclose a square, there is 1 bead. I made the background black and then assigned a color to each column. The rainbow is because I am gay, of course. :]

[mrvelocipede]

wow, has it really been a year since the internet discovered Goncharov?

[tres13]

FULLVIEW for best quality; Tumblr nukes all my image uploads!

For this year’s (2023) DannyMay, prompt “Fractals”

Experimenting with drawing/painting styles, with my current favorite subject. :D

And the version with just the cool, starry stuff, no clock/gear motifs:

[the-noxxi]

Fractals in Meme-nutes:

Urban Battlegrounds

The second part of the fractal meme mini series. Hope you guys enjoy! 😅

Youtube link

[chasingrainbowsforever]

Always From Here to Infinity ~ Julia Fractals