#fractal mathematics

[rbrooksdesign]

∑FEETc: Divisor Matrix Table (DMT) 19, digital painting, June 19, 2025, Reginald Brooks

∑FEETc

*Fractal

*Entanglement

*Entropy

*Time

*Consciousness

[smashorpassobjects2]

[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.

[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. :]

[bluetoad07]

i made a new (?) fractal today!

i call it the burning duck :3

v [explanation below!] v

i have no idea if anyone else has seen this before (someone probably has), but i think it's really cool!

this is somewhat of a halfway point between the mandelbrot set and the burning ship. the original burning ship fractal is the result of taking the mandelbrot set's equation ( z = z^2 + c; where z and c are complex numbers ), but using the absolute value of z instead ( z = |z|^2 + c ).

the result is this, a very pretty fractal that is quite well known:

while experimenting with my own fractal renderer i've been working on, i realized that i didn't have to absolutize the entirety of z. because it's a complex number, the real and imaginary portions are stored in separate variables, so i tried to see what happens if you only do one of them!

absolutizing the real half was very boring, it just mirrored the bottom half of the burning ship to the top. but the imaginary half created the duck!

visually, i think this is probably my favorite fractal! i am very surprised how unique it is to the burning ship despite being so closely related. here's a couple really pretty screenshots i took:

anyways thanks for reading this!!

[anarthursworld]

The Frondity Substack explores the connotations of a fractal universe. The link takes you to pages 8 To 15 containing The Journey Begins post of the Frondity publication.

[hyperoperationfractallisation]

Fractals don't just have finite area.

They have zero area.

[looseartist]

ma 0_0 low res

[daily-public-domain]

Day 389: Fractal Tree, 2005

link

–This image is part of the public domain, meaning you can do anything you want with it! (you could even sell it as a shirt, poster or whatever, no need to credit it!)–

[rbrooksdesign]

∑FEETc: Divisor Matrix Table (DMT) 26, digital painting, May 26, 2025, Reginald Brooks

∑FEETc

*Fractal

*Entanglement

*Entropy

*Time

*Consciousness

[citheroniaregalis]

Don’t care + didn’t ask + I was emotional about fractals before you had even discovered what religious symbolism was + I have natural DD cups

[fuckyeahfluiddynamics]

Why Nature Loves Fractals

Trees, blood vessels, and rivers all follow branching patterns that make their pieces look very similar to their whole. We call this repeating, self-similar shape a fractal, and this Be Smart video explores why these branching patterns are so common, both in living and non-living systems. (Video and image credit: Be Smart) Read the full article

[williammorrised]

Bi & z → z(1/c - 1)(1 - z) @ (-0.85 + 0i)

Trying out some new complex functions to get more "flag-like" shapes. It's difficult to get the scale right and keep the detail, but it's fun to try!

— Own work, 2023 (CC0)

[noosphe-re]

Every scrap is a fractal.

Ahmed Salman

[breofannasullivan]

Shop :: Displate | InPrnt

Socials :: Website | Bluesky | Tumblr

Old Art, pre-2021. Created with a mixture of Apophysis 7x, Chaotica and Ultra Fractal 6.

[blake447]

I realized I hadn't shared this here yet! Here's my 3D printed Quaternion Julia Set! See I first learned of these things reading about it from a pretty well known graphics programmer Inigo Quilez. Theirs are a lot prettier! But yeah, if you're familiar with Julia Sets and the Mandelbrot set already, this is basically that but we use 4D complex numbers called quaternions instead of the regular old complex numbers.

The original shaders I used to render them were unity CG/HLSL implementations, but this particular one is from a GLSL implementation over on my shadertoy you can find here: https://www.shadertoy.com/view/tdt3W8 It isn't exactly the same one that I've printed here (I've long lost the exact seed) but it is reasonably close. The way I printed it was I stole some marching cube code for blender and just plugged in the SDF function derived by Inigo Quilez, tweaked the values and eventually got a mesh I can print!

This uh, isn't the one I used lol. It did take a few tries to get one that was both visually interesting and also printable. In fact i wasn't even using the marching cube algorithm at first. I was using Poisson Surface Reconstruction with a python script that casted points to form a point cloud. Basically I was attempting to create a mesh like you would with photogrammetry, just with an abstract object rather than an actual thing or place.

The results were, well not good lol.

*Continues digging through box* I know its around here some where, I should have the one that works. Okay this still isnt it but this one is using the same method, I just wanted to use this for a vrchat world instead of using it for 3D printing. It gets the point across lol

But yeah. 3D printing is really cool if you're into a bit of math