Marcus Volz

Presenting Math Art Part 1: Cellular Automata | Fractals | Artificial Life | Computational Systems. An 11-minute video featuring animated visualizations of iconic structures in mathematics and computation, created with #houdini and #redshift3d. youtu.be/P3UjXGW7PFA

Featuring systems by @stephen_wolfram @wolframphysics @zzznah @SoftologyComAu @slackermanz and many more.

Presenting Math Art Part 1: Cellular Automata | Fractals | Artificial Life | Computational Systems. An 11-minute video featuring animated visualizations of iconic structures in mathematics and computation, created with #houdini and #redshift3d. youtu.be/P3UjXGW7PFA

Further experiments with 3D continuous CA based on the system by @stephen_wolfram wolframscience.com/nks/p155--cont… Continuous cell states in [0, 1]; updated state = fractional part of (avg neighbor state + a constant); 6 neighbors; cells with states below a threshold are not drawn.

3D totalistic cellular automata with spherical neighborhoods. Neighboring cells are within a sphere of radius r, for r=Sqrt[2] (between von Neumann and Moore), 2 and Sqrt[6], on a grid with 1 unit spacings. Cells with exactly one active neighbor become active. Steps: 120-240.

Edit: 8 and 20 neighbors

Hexagonal prism totalistic cellular automata with 6 and 26 neighbors run for 240 steps starting from a single live cell, using the space-filling hexagonal grid systems described by @SoftologyComAu and @francisbitonti. softologyblog.wordpress.com/2020/06/03/hex… demonstrations.wolfram.com/HexagonalPrism…

Two-color 26-neighbor totalistic cellular automata run for 240 steps starting from a single live cell. The first rule is from NKS p. 183 by @stephen_wolfram; in the second rule a cell becomes live if it has either one or three live neighbors. wolframscience.com/nks/p183--cell…

Hypergraph rewriting based on systems and rules from the @wolframphysics Registry of Notable Universe Models: wolframphysics.org/universes/

3D geometry constructed from bitwise functions applied to x,y,z integer coordinates, based on the x,y systems by @stephen_wolfram in NKS p. 871. Cubes with values below a threshold are not drawn. wolframscience.com/nks/notes-2-1-…

Generalized mobile automaton with rule set (f) from Page 77 of NKS by @stephen_wolfram, run for 5000 steps wolframscience.com/nks/p77--mobil…

3D continuous cellular automata based on the system by @stephen_wolfram in NKS wolframscience.com/nks/p155--cont… Continuous cell states in [0, 1]; new state = fractional part of (avg neighbor state + constant); von Neumann neighborhood; cells with states below a threshold are not drawn.

The Rössler attractor, implemented with VEX in #houdini from equations and parameters in the Wikipedia article: en.m.wikipedia.org/wiki/R%C3%B6ss…

H tree fractal, implemented with VEX in #houdini from the description in the Wikipedia article: en.wikipedia.org/wiki/H_tree

Pathlines across vector fields starting from scattered points on parametric surfaces (Saddle Torus, Horn, Antisymmetric Torus). Surface equations are from the parametric surfaces and bodies section on Jürgen Meier’s homepage (3d-meier.de). #houdini #vex #redshift3d

Fractals constructed from Platonic solids (dodecahedron, icosahedron, cube) by recursive scaling and copying onto vertices. Implemented procedurally with #houdini based on fractal construction and animation techniques by PurpleCat: youtube.com/watch?v=8bDYk5…

Gray-Scott reaction diffusion simulations on a plate, etched and embossed. Implemented with VEX in #houdini from the descriptions and parameters provided in the article by Karl Sims and the video by Neat AI: karlsims.com/rd.html m.youtube.com/watch?v=r9iBGV…

Boids (flocking) simulation on the surface of a Dupin cyclide. Implemented with VEX in #houdini from the description on Craig Reynolds’ Boids page: red3d.com/cwr/boids/ en.wikipedia.org/wiki/Dupin_cyc…

Diffusion-limited aggregation in three dimensions implemented with VEX in #houdini based on the neighbor counting technique described by @SoftologyComAu softologyblog.wordpress.com/2016/08/29/dif…

Hilbert, Gosper and Peano space filling curves on the surface of the Borromean rings. Implemented using L-Systems and equations from the following resources: robertdickau.com/lsys2d.html paulbourke.net/fractals/lsys/ paulbourke.net/geometry/borro… #houdini #vex #redshift

Three-color totalistic cellular automata on the surface of variants of the Klein bottle. System and rules are from A New Kind of Science pp. 60-70 by @stephen_wolfram wolframscience.com/nks/p60--more-… #houdini #vex #redshift3d