#fractal

[vedalkensamurai]

Six linear orbit traps run along the real axis. They spread out like a fan, staying fixed at the origin, then collapse along the imaginary axis.

[hacknyc]

two

[wolframcarbide]

[androgynouspear]

Women aren't usually my cup of tea BUT Goddam!! Look at the CURVES on julia!💘😩🤭

GOD she so mathematically intirciate I'm DROOLING 🤤 😋 😩 😫

Just look what she's got hidden under there ❤️

Hnnnn you can rotate her in SIX diffrent dimensions she Is just so Flexible 😉 😜 😘 😉 😜 😘

Ohh my god QUEEN you contain the mathematical beauty of the universe in you

Is it just me or is it getting hot in here!!

I need her too step on me so bad

[jfyfractal3]

See : https://jfyfractal3.tumblr.com/image/790955501135478784

[webdiggerxxx]

꧁★꧂

[violetfractal]

You can generate Sierpiński 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”.

Original Date May 7th, 2023 11:16pm

[turbofanatic]

It's not that her sword is black, more that it cooks most optical sensors.

[xponentialdesign]

MandelbROOTS

[basnih-gifs]

Opaline Vein.

[848ellie]

Hippie nostalgia

[vedalkensamurai]

A lone knight sits in the center of the board. It gives birth to eight offspring, who each move away either two cells vertically and one horizontally, or one vertically and two horizontally, as is traditional for knights. The parent knight grows old and dies, and the young knights mature and give birth to offspring in their turn. But if two baby knights try to occupy the same cell, they compete for resources and neither survives past infancy.

[hacknyc]

persist

[wolframcarbide]