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Visualising a 4-dimensional fractal.  A Sierpinski triangle is an infinitely detailed picture created by recursively removing the inside of triangles. In 3 dimensions you recursively remove the insides of triangle based pyramids (tetrahedra) to get a similar picture. Here the 4-dimensional analogy is shown rotating. Note the shape is not being deformed, but it is simply being projected into 3 dimensions as it rotates in 4 (just as the shadow of a cube appears to deform as the cube is rotated). [code] [more]

Visualising a 4-dimensional fractal.  A Sierpinski triangle is an infinitely detailed picture created by recursively removing the inside of triangles. In 3 dimensions you recursively remove the insides of triangle based pyramids (tetrahedra) to get a similar picture. Here the 4-dimensional analogy is shown rotating. Note the shape is not being deformed, but it is simply being projected into 3 dimensions as it rotates in 4 (just as the shadow of a cube appears to deform as the cube is rotated). [code] [more]

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Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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