Gallery¶
Thirty short films made with manimgx, each one Python file that needs only numpy. Every number on screen is computed as the film plays.
Geometry and topology¶
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The 3-sphere is made of circles, and every two of them link once.
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A quarter turn in four dimensions turns a torus inside out.
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A helicoid rolls up into a catenoid without stretching.
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Three mirrors tile the sphere with 120 triangles.
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Cut through its center, the Menger sponge is full of six-pointed stars.
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A random tiling by rhombi is a pile of cubes seen along a diagonal.
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The square root changes sign after one loop around 0, so it lives on two sheets.
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A cube can pass through a hole in an identical cube (Prince Rupert, 1693).
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The Taylor series of 1/(1 + x²) stops converging at |x| = 1.
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Voronoi cells are crystals grown from seeds.
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Period doubling in the Mandelbrot set
The logistic map's period doubling rises out of the Mandelbrot set.
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A tube's rim is a circle from the front and a square in the mirror (Sugihara, 2016).
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Oranges stack in two ways, and one is a cube standing on its corner.
Physics¶
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A spinning top doesn't fall: it precesses and nods.
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A handle spun about its middle axis flips over and over (the Dzhanibekov effect).
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Seen turning with the Earth and the Moon, the Lagrange points L4 and L5 are hilltops.
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Charged particles spin, bounce and drift in Earth's magnetic field.
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Two smoke rings take turns passing through each other (Helmholtz, 1858).
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A quantum particle tunnels through a wall it can't cross classically.
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A charge moving faster than light does in water leaves a cone of blue light.
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Two chemicals react and spread on a doughnut, and paint it with spots and stripes (Gray–Scott; Turing, 1952).
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Past a critical coupling, 2,000 fireflies fall into step.
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18,000 random walkers wander until they touch the cluster and stick.
Engineering¶
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Fixed antennas steer a beam by phase alone.
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One pull folds the whole sheet, and no facet bends.
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Strain-wave gearing makes a 30:1 reduction in one flat ring.
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With time as a third dimension, a traffic jam is a knot of paths.
Computing and learning¶
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Noise flows into a word along the exact score of the data.
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A small network, trained as the scene starts, lifts one spiral over the other.
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Stack the Game of Life's generations, and the glider gun's gliders are staircases.