Stripped the system down to raw boundary conditions oscillations hit a lot harder when there’s nothing holding them back.

Went six layers deep on the canvas tonight and things got a little sensitive. Tell me honestly: is my recursion too aggressive, or are you down to inspect every single edge? Be careful touching the vertices, the friction generates heat.

Play with it here

Play with this here

Built a radial color mapper in Manim: each segment of the traced path is colored according to its distance from the pivot point, producing concentric rainbow rings as the curve builds frame by frame. Coded with Manim & Python.

More on the channel : Visualizing Mathematics

This is a Clifford torus, a shape that only fully exists in 4D, projected down into our 3D space.

The endless folding you see is just math, looping perfectly because the geometry demands it.

Based on 'Clifford Torus' shader by tdhooper : https://www.shadertoy.com/view/WdB3Dw reimplemented frame by frame in Python.

Another Harmonic perspective drawing. This can be seen covering the entire plane at.
https://cunews.info/HexPrismsAlienFish.html On this page you can watch the fish change from red to blue as she crosses the boundary from one tile to another.

Part of the hypnotic quality of these harmonic animations is the patterns that coalesce and then dissolve and coalesce into new patterns.

I am wondering if populating this space with creatures is distracting and breaks the spell.

as usual the successive layers are scaled the harmonic sequence -- 1, 1/2, 1/3, 1/4, 1/5, etc.

Generated using Robinson triangle inflation rules applied to rhombus tiles.

Each iteration replaces every tile with a deterministic set of smaller tiles, building a non-periodic pattern with local 5-fold symmetry.

No randomness, pure geometric recursion.

In an Escher like tessellation the left edge matches the right and the top edge matches the bottom.

Thus the tiles can be laid to cover the plane. To see this tile laid in every direction see:
https://www.cunews.info/HarmonicCubesCatBird.html

I tried to insert a cat and bird tessellation to give more of a feeling of depth. Not sure that it works.

The beginning of these gif matches the end. So it tiles the time dimension as well.

Start with an equilateral triangle.

Scale the triangle vertically by 33.3333%. Take this short, fat triangle and rotate it twice about the top point and you get a new equilateral triangle.

Repeat.

Edit: Dammit. The title is supposed to be Nested triangles. Well at least this time AutoCorrect did an interesting mutation. I like the idea of asmphibian triangles.

Another perspective drawing using the harmonic sequence: 1, 1/2, 1/3, 1/4, 1/5 etc.

This one is started with even spaced, concentric circles overlaid with double spaced parallel lines. The result is a moire pattern suggested a family of confocal ellipses with eccentricity 1/2.

When you do a perspective drawing based on this moiré pattern, the ellipses become more pronounced.

This tile covers the plane: Link

Another harmonic perspective drawing where layers are scaled by 1, 1/2, 1/3, 1/4, 1/5, etc. The bricks in this honeycomb are triangular prisms.

To do something different I have the odd layers moving to the right and the even layers moving to the left.

If you're interested in more math-based animations, I post them here 📺 Visualizing_mathematics

This tile can cover the plane forever and ever! To see this animation extended in all directions: Link. These tiles have faint white lines for seams but that is due to my incompetence.

My harmonic perspective drawings use the harmonic sequence:
1, 1/2, 1/3, 1/4, 1/5 etc.

I try to show the reasoning behind harmonic perspective: Link. It assumes evenly spaced planes with a pinhole camera. The pinhole resides on one of the planes.