u/USedona

A 3D Menger Sponge : infinite surface area, zero volume

Ten hexagonal rings, spinning until the screen fills edge to edge.

Hey,

Currently mounting a 43" 2025 Frame TV using the paper template, but the diagram is throwing me off. As you can see on the paper : The lower corner guides (┌ and ┐) show the top edge of the TV in landscape. But right above them, there’s a second set of corner.

If the lower pair already marks the top of the TV, what is the higher pair for? Is it for the extra clearance when dropping the TV onto the hooks?

Thanks

Coded with Python.

Here's the result.

Just a smooth loop of Stitch going through a continuous sequence of geometric distortions and conformal mappings. Calculated purely through code, no keyframes or manual warping !

Playlist link : Perfect loops 🔁

Zoom in. Rotate. Repeat. Forever.

The Vicsek fractal keeps the same pattern at every scale, this is what a fractal dimension of 1.465 looks like in motion.

Coded with Python & OpenCV.

YouTube version (4K 60fps) : Vicsek Fractal

Most people expect chaos from a double pendulum. But if both arms rotate at constant angular velocity, the result is pure deterministic symmetry. Change the ratio, change the number of loops : it's that simple. Coded with Manim & Python.

More on the channel : Visualizing Mathematics

A recursive algorithm, iterated as the curve winds through the entire volume of a cube.

Each step replicates the previous shape 8 times : order 5 already generates 32,767 connected segments, all from a single continuous line.

Full video : Generative 3D space-filling curve

I’ve been trying to understand the exact geometry of the panels of the Adidas “Trionda” football.

From what I can tell, the design is based on a tetrahedral structure mapped onto a sphere (or at least strongly tetrahedral symmetry). This seems fairly consistent across visual evidence.

However, I’m struggling with determining the exact shape of the panel seams.

I don’t understand the geometry behind the images circulating online, such as this one : picture

In particular, I cannot derive:

- the exact mapping used from the polyhedral structure to the sphere,

- the analytical form (if any) of the seam curves on the spherical surface,

- nor the planar development (2D pattern of a single panel).

My suspicion is that many of the SVG / vector reconstructions online are approximations rather than the true underlying construction.

Does anyone know if there is a known mathematical model for these panels) ?

Thanks ! ⚽

Remove the center. Repeat forever.

The Sierpiński carpet starts with a single square and, with one recursive rule, punches an infinite number of holes into it.

The Mandelbrot set, zoomed out thirty-six octillion times.

At this depth, the boundary keeps revealing new structure, the same chaos echoing at every scale.

I animated an epicycloid in Manim with a fixed circle of radius R=3.5 and a rolling circle of radius r=0.7 (R/r=5), and counted 7 cusps instead of the 5 I expected.

Working through the parametrization, the relative angular speed between the traced point and the rolling circle's center comes out to (R+2r)/r = 7, not R / r = 5 or even (R+r)/r = 6. The extra +r seems to come from the direction convention for the point's rotation on the rolling circle (I parametrized it rotating in the same direction as the orbit rather than the more standard opposite direction).

Is there a clean geometric way to see why this specific convention shifts the cusp count from (R+r)/r to (R+2r)/r? Or is this a known distinction between different epicycloid parametrizations that I'm just not aware of?

x(t) = (R+r)cos(t) − r*cos((R+2r)/r*t)

y(t) = (R+r)sin(t) − r*sin((R+2r)/r*t)

This is the "Butterfly Curve", discovered by T. Fay. I used Python and Manim.

This curve is defined by a polar equation involving exponential and trigonometric functions.

The animation plots the curve as a function of t between 0 and 2π