#3d fractals

[webdiggerxxx]

꧁★꧂

[daily-public-domain]

Day 393: Mandelbulb Fractal (this image is so big I had to downscale it, full resolution is 48.97MB)

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!)–

Zoom anywhere and you've got a new wallpaper!

[blockygraphics]

MANDBOX.GIF, from the Desktop Publishing Shareware Breakthrough CD (1993) via cd.textfiles.com. Bottom right appears to read "ESP 3/90"; other info/artist credit appreciated. Based on the filename the fractal is probably the Mandelbrot set.

[violetfractal]

I used excel to generate some 3 dimensional analogues of the Sierpiński gasket, then constructed the outputs in Minecraft :D

These fractals are embedded in 3D space, but they are not themselves 3 dimensional:

The diorite structure (left) has fractal dimension log_2(5) ≈ 2.3 (since each unit consists of 5 subunits at 1:2 scale).

The granite structure (right) is built from 4 half-scale copies of itself, so bizarrely its dimension is log_2(4) = 2.

As a consequence of its low dimension the 16x16x16 structure has a volume of just 16^2 = 256 blocks. The other fractal, also 16x16x16 but 2.3 dimensional, has a volume of 625. That’s beefier than the 2D one, but a solid 16x16x16 3D cube would dwarf it with V = 4096.

Finally, since this blog is msexcelfractal and not msminecraftfractal, here’s the formula and blueprints I used for the 2.3D structure.

Original Date: June 9th, 2023 9:56pm

[rivka-kopelman]

[jfyfractal3]

See : https://jfyfractal3.tumblr.com/image/778367488048136192

[arcanaexe]

[uefiser]

[wolframcarbide]

[talos-stims]

zooming in on a fractal tree | source

[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

[orange-blob-of-pixles]

This fractal I printed looks like the time room

[dimalink]

It is time to drink a tea!

Rabbit invites everyone to drink a tea. Tea at the evening, rabbit every day gives everyone a call for friends to go for a tea at the evening. And kind and good little animals. And different aliens. Everyone who have some interest. At the tea. Every evening. Rabbit says – It is time to drink a tea! And this is magic place. Magic field. So, mushrooms are here. And there is a table and lots-lots of little chairs. To sit down every good and kind little animal.

You can go with your tea. And rabbit has his own tea.

Rabbit says – it will be soon a time to drink a tea!

All good and kind animals will go. Little mouses, grasshoppers, snails, bugs. Mole will come. Squirrel will come. Cat will come. Everyone will come. In this magic place humans also sometimes to appear. And aliens. Too.

In this place everything is multidimensional and time too. It flow as it is like at the one moment. Or everything starts and ended also. So, it depends what time line you to enter. There are millions of different fields. It is like endless fractal – it is space and time. Everyone can go for a tea, as you wish! Time has no meaning!

You can sit down at the mushroom to look around everything. And to choose a right time and place to drink a tea!

Dima Link is making retro videogames, apps, a little of music, write stories, and some retro more.

WEBSITE: http://www.dimalink.tv-games.ru/home_eng.html ITCHIO: https://dimalink.itch.io/ GAMEJOLT: https://gamejolt.com/@DimaLink/games

[blockygraphics]

FRACSPRL.BMP, modified July 23, 1997, 11:07 AM; image from the 1997 CD-ROM Real World Bryce 2: The Art of the Digital Landscape.

[violetfractal]

Built a 3d analog of the rule 150 fractal. Got bonus planar fractals:

the central orthogonal planes are rule 150 automata.

the sloped outer faces are Sierpiński gaskets.

the lateral cross sections are periodically self-similar “graboids."

Original Date: June 14th, 2023 9:25pm

[rivka-kopelman]