Non-Euclidean Dreamer

Pure Translation Space Group

Stacked Wallpaper Patterns for this Month's High-resolution Render for Patrons of Level Square and up! Full Resolution: 25600x14400px

Throwback to August 2012 #creativecoding youtu.be/O6Un816f51c

Lensing #mathsky

Stacked Wallpaper Patterns for this Month's High-resolution Render for Patrons of Level Square and up! Full Resolution: 25600x14400px

Fifth Dihedral Group #mathart

#mathsky

Cayley Graph of the Heisenberg Group! Full Version: youtu.be/N6zfQBOoMOg #creativecoding

Cayley Graph of the Heisenberg Group! Full Version: youtu.be/N6zfQBOoMOg #creativecoding

Order 7 Cyclic Group #codeart

Order 7 Cyclic Group #codeart

Full Octahedral Symmetry Group #mathart

Full Tetrahedral Symmetry Group! #mathart

Full Tetrahedral Symmetry Group! #mathart

of course there is no chance for the free group F2 to steer clear of itself in the Euclidean plane. Time for Cayley-Graphs to go 3d!

of course there is no chance for the free group F2 to steer clear of itself in the Euclidean plane. Time for Cayley-Graphs to go 3d!

Trying something 3d Koch snowflaky... #fractalfriday #codeart #creativecoding

3d Line Group generated by a 90° glide-rotation

Assembling the Cayley Graph of the Group <a,b|a^3,b^3,(ab)^3> Watch it crystallize in the full version: youtu.be/BVIcFy6d6PM

pumping the middle of the triangle with a wavelength equal to the incircle radius, then letting it go. #mathsky

Assembling the Cayley Graph of the Group <a,b|a^3,b^3,(ab)^3> Watch it crystallize in the full version: youtu.be/BVIcFy6d6PM

Chiral Tetrahedral Symmetry Group

Well this is getting out of hand... #creativecoding

Exploring Waves passing through lenses. Full Musical Video: youtu.be/cEoTLYnajNo #creativecoding #mathsky

Frieze Group p11g #mathart

Frieze Group p11g #mathart

First trial run for my Cayley Graph implementation. Cyclic Group of order 4. #math

First trial run for my Cayley Graph implementation. Cyclic Group of order 4. #math

My Patrons are voting on my November Theme! The Options are: CA Rule Play Non-Euclidean Geometry General Relativity www.patreon.com/posts/172272...

Frieze Group p1m1

Frieze Group p1m1

Frieze Group p2mg

Frieze Group p2mg

Frieze Group

Going 3d wit chiral octahedral symmetry...

This wavelength is two thirds of the square's diagonal. It does not give a standing wave. #mathart

Going 3d wit chiral octahedral symmetry...

Dragon Trigon Tiling: A kite gets divided into two kites and one triangle, a triangle gets divided into three kites. #creativecoding #mathart #fractal

A wavelength of exactly the field's side length. I enforce it in the middle for two lengths then let go. Tada, a standing wave. #mathart

The Symmetry Group of a uniform triangle: The Dihedral Group of order 3. #mathart

The Symmetry Group of a uniform triangle: The Dihedral Group of order 3. #mathart

The integers.... The infinite cyclic group...

Two sources, two frequencies #mathart

The integers.... The infinite cyclic group...

Full Journey through all 17 Wallpaper Groups: youtu.be/iSOq7_185fI #mathart

I model these symmetry groups with matrices. But how can I write a translation as a matrix? My trick is to shift the plane into the 3d dimension, then the matrix (1 0 1 0 1 0 0 0 1) acts as a translation in x-direction on that affine plane. Here we have D_infinity.

I model these symmetry groups with matrices. But how can I write a translation as a matrix? My trick is to shift the plane into the 3d dimension, then the matrix (1 0 1 0 1 0 0 0 1) acts as a translation in x-direction on that affine plane. Here we have D_infinity.

Shifting Colors in the Fish Tiling #creativecoding #mathart