6 Infinite Patterns That Will Melt Your Brain

Explore the mesmerising world of visual mathematics as we animate four infinite fractals from first principles.

In this animation, we strip away complex equations and look purely at the geometry of recursive growth. Starting with a simple grid, we visualise how a single mathematical rule, repeated infinitely, creates perfectly self-similar structures.

The fractals visualized in this video include:

The Sierpinski Carpet (The "Woven Fabric")

The Blueprint: Picture a perfect square tile. Now, slice it into a tic-tac-toe grid and punch out the middle square so you can see right through it.

The Action: Take the 8 remaining outer squares and punch the exact same hole in the middle of every single one of them.

The Visual: As you zoom in, it looks like an infinitely porous sponge or a deeply woven digital fabric that becomes lighter and lighter.

The Sierpinski Triangle (The "Triforce")

The Blueprint: Start with a solid, upward-pointing triangle. Cut an upside-down triangle directly out of its center, leaving you with three smaller triangles in the corners.

The Action: Treat those three new corner triangles as brand-new starting blocks, and scoop the middle out of them, too.

The Visual: It creates an endless, mesmerizing pyramid built entirely out of hollow, microscopic pyramids.

The Quadric Cross (Vicsek Fractal)

Built on a 3x3 grid, this pattern retains only the center and cardinal edges. At each step, the dimensions shrink by an exact 1/3 scaling factor, resulting in a 5:1 replacement ratio that mimics digital circuit boards.

The T-Square Fractal

An additive fractal that explodes outward. By placing new squares perfectly centered on the exposed corners of the parent shape, the dimensions scale down by 1/2 at each level, creating a dense architectural blueprint.

The Hexaflake

A perfect demonstration of 7-hexagonal packing. By using a 1/3 linear scaling factor, we can pack six regular hexagons around a central seventh hexagon, mimicking the natural crystalline symmetry of snowflakes.

The Pentaflake (Sierpinski Pentagon)
Unlike hexagons, pentagons cannot tile perfectly on a flat plane without leaving gaps. To create flush, non-overlapping edges, the central pentagon must be rotated 180 degrees, and the entire structure must scale down precisely by the inverse of the Golden Ratio (approximately 0.382).

Sit back, relax to the soft jazz, and enjoy the infinite loop of first principles geometry.

Chapters:
0:00 The Sierpinski Carpet (1/3 Scale)
0:15 The Sierpinski Triangle (1/2 Scale)
0:37 The Quadratic Cross (1/3 Scale)
0:54 The Hexaflake (1/3 Scale
1:09 The T-Square Blueprint (1/2 Scale)
1:30 The Pentaflake & The Golden Ratio (0.382 Scale)

Видео 6 Infinite Patterns That Will Melt Your Brain канала Barely Converging 😏