#quaternion Julia set fractal

[wolframcarbide]

[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

[tactile-math]

Builds by Z Corp Z 510 Color 3D Printer at the Visualization, Media and Imaging Laboratory (VMIL) of the Imaging Technology Group (ITG) Beckman Institute University of Illinois at Urbana-Champaign and on FormLabs by CKC1010

[numb3rth30ry]

Ethereal quaternion Julia set cross-sections. You remember our friends, the quaternions, yes?

Mathematics is beautiful. <3

Source 2: http://www.juliasets.dk/Quaternion.htm

[zouassi]

instagram.com/Zouassi

[art-now-germany]

# 2016 Fractal art Original...., Igor Bajenov

# 2016 Fractal art Original! Exclusive Photo Collection Design in Contemporary Art -Digital Photo Mix -Abstract / Geometric-Figurative Art Deco in Fine. A detail from a non-integer Multi bread set Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as StillImages, animations, and media. Fractal art developed from the mid-1980s onwards. [1] It is a genre of computer art and digital art Which are part of new media art. The Julia set and Mandelbrot sets can be Considered as icons of fractal art. [2] Fractal art (especially in the Western World) is not drawn or painted by hand. It is created Usually Indirectly with the assistance of fractal-generating software, iterating through three phases: setting parameters of Appropriate fractal software; Executing the Possibly lengthy calculation; and Evaluating the product. In some cases, other graphics programs are used to modify the images produced Furtherwirt. This is called post-processing. Non-fractal imagery may therefore be integrated into the artwork. [3] It was Assumed That Fractal art Could not have developed without computer Because of the calculative capabilities They Provide. [4] Fractals are generated by applying iterative methods to solving linear equations or polynomial non-equations. Fractals are any of various extremely irregular curves or shapes for Which any suitably chosen part is similar in shape to a larger or smaller part Given When magnified or reduced to the SameSize. [5] A 3D Mandelbulb fractal generated using Visions of Chaos There are many different kinds of fractal images and can be subdivide into several groups. Fractals derived from standard geometry by using iterative transformations on at initial common figure like a Straight Line (the Cantor dust or the Koch curve), a triangle (the Sierpinski triangle), or a cube (the Menger sponge). The first fractal figures invented near the end of the 19th and early 20th centuries belong to this group. IFS (iterated function system) Strange Attractors Fractal Flame L-system fractals Fractals created by the iteration of complex polynomials: Perhaps the most famous fractals. Newton fractals, Including Nova fractals Quaternionic and (Recently) hypernionic [clarification needed] fractals [6] Fractal terrains generated by random fractal processes [7] Mandelbulbs are a kind of three dimensional fractal. Fractal expressionism is a term used to differentiate traditional visual art did Incorporates fractal elements: such as self-similarity for example. Perhaps the best Example of fractal expressionism is found in Jackson Pollock's dripped patterns. They have been found to contain a Analysed and fractal dimension Which has been attributed to his technique. [8] Techniques [edit] Fractal image generated by Electric Sheep A fractal image made with Sterling Fractals of all kinds have been used as the basis for digital art and animation. High resolution color graphics Became increasingly available at Scientific Research Labs in the mid-1980s. Scientific Forms of Art, Including fractal art, have developed separately from mainstream culture. [9] Starting with 2-dimensional details of fractals: such as the Mandelbrot set, fractals have found artistic application in fields as varied as texture generation, plant growth simulation and landscape generation. Fractals are sometimes combined with evolutionary algorithms, Either by iteratively choosing good-looking specimens in a set of random variations of a fractal artwork and Producing new variations, to avoid dealing with cumbersome or unpredictable parameters, or collectively, as in the Electric Sheep Project, where people use fractal flames rendered with distributed computing as Their screensaver and "rate" the flame They are viewing, influencing the server, Which Reduces the traits of the undesirables, and Increases Those of the desirables to produce a computer-generated, community-created piece of art. Many fractal images are admired Because of Their perceived harmony. This is Typically Achieved by the patterns Which emerge from the balance of order and chaos. Similar qualities havebeen described. In Chinese painting and miniature trees and rockeries [10] Fractal rendering programs used to make fractal art include Ultra Fractal, apophysis, Bryce and Sterling. Fractint what The First Widely used fractal generating program.

https://www.saatchiart.com/art/Photography-2016-Fractal-art-Original/462428/2806575/view

[mathart]

3D Fractal Zoom turned 2 today!

[karoltabis]

a little compilation of experiments and tests with houdini volume procedural shader there are: basic mandelbrots 3d mandelbulbs with random julia sets ( 2-complex pow formula from wikipedia) https://ift.tt/1v2ukdE mandelbox formula i googled somewhere on fractal forums and wikipedia https://ift.tt/1yyH1w6 4d fractal is based on classic quaternions algebra coloration logic is made up on the go render times vary from 10-15 min per frame on 3d fractals to 40-80 min per frame on hard divings, that's why there are not too much of them, and some are in lower resolution link to the paper for double precision emulation with floats: https://ift.tt/2qxHl0f actual vex include files are here: https://goo.gl/uvaBP2 fractal hips are pretty messy, unfortunately, so i'll be cleaning up and posting here some files as time goes. shattering fractals hip: https://goo.gl/lcnBtS . I cleaned it up and left some notes and vex comments on how what stuff works. And here are the dirty files. oh, really messy and dirty, you can follow the logic of cleanedup file(s) to navigate though the nightmares of these scenes: https://goo.gl/ye9OMi

[wolframcarbide]

[wolframcarbide]

[wolframcarbide]

Quartered sections of 3D slices through a quaternion Julia set fractal, Qn+1 = Qn * Qn + 0.5 - 0.3i + 0.0j + 0.0k + 0.0l.

[wolframcarbide]

[wolframcarbide]

[wolframcarbide]

[wolframcarbide]

[wolframcarbide]