matthen

The focus of a rolling parabola traces out a catenary, the curve of a hanging chain held by its ends. [code] [more]

In MC Escher’s Metamorphose, he transforms square tiles into hexagons by manipulating his iconic lizard pattern. These then go on to become honeycombs and three dimensional buildings. Inspired by Escher, this animation also alternates between a chessboard and a three-coloured hexagonal tessellation, and between 2 and 3 dimensions. [code]

Each square growing out from the centre is rotated a fixed angle from the previous one. For most angles, this creates visible structure such as defined spiral arms. But at the golden angle the corners are spread out relatively evenly. Nature takes advantage of this in plants like the Romanesco Broccoli to evenly spread out the disgusting-tasting broccoli florets as they grow. [code] 

Each disk is ten times larger than the previous one. If the first disk you see is the size of the palm of your hand, then the second is the size of a coffee table, the third the size of a room. The seventh is the size of Belgium. The ninth is the size of the Earth. The 23rd is around the size of the galaxy, and less than 2 minutes into watching, the 28th is the size of the Universe.   [code]

This spiral is rotated by the golden angle every frame. Though it looks like the circles are growing and changing colour, they are actually unchanging and the whole image is just rotating. [inspired by these amazing sculptures] [code] [related]

For any triangle, you can draw a circle that fits perfectly inside (the incircle) and also one that connects all its corners (the circumcircle). This shows the path of the centre of the incircle, as a triangle is shuffled around its circumcircle. [code]

Connecting all points a varying distance apart along a triangular wave, revealing a variety of smooth curves. Inspired by Henry Moore’s mathematical sculptures. [code]

Visualising numbers (100, 243 and 12) by splitting them into all possible factorisations. [code]

Rotating a circle around one of half its radius to create a heart-shaped cardioid curve. [code]

The period of each pendulum is a whole number multiple of an underlying length of time. This means that they periodically line back up to their starting positions. But between points where they line up, they create patterns - grouping up into two groups, three groups as well as appearing chaotic. [inspired by] [code]

8 Earth years are roughly equal to 13 Venus years, meaning the two planets approximately trace out this pattern with 5-fold symmetry as they orbit the Sun. [more] [code]