This seems to be everyone's favorite three-dimensional fractal, so much
so that I've had to add a separate page for it and several other closely
related fractals. The Sierpinski Tetrahedron has Hausdorff dimension
two, so maybe it's not really a fractal in the "fractional dimension"
sense of the word. It can be formed in many ways: (1) start with a
single tetrahedron and remove octahedra from it, (2) recursively combine
quadruples of tetrahedra into larger tetrahedra, (3) take "Pascal's
Pyramid" of trinomial coefficients modulo two, (4) form the graph of the
binary exclusive-or function on the unit square. The last construction shows
that if you look down on it from the right direction, it just looks like
a square, but from other viewpoints it has plenty of holes, so it can
form a sort of "Venetian blind" that casts shadows only in certain
directions.
Fun with Fractals and
the Platonic Solids. Gayla Chandler places models of polyhedra and
polyhedral fractals such as the Sierpinski tetrahedron in scenic outdoor
settings and photographs them there.
IFS and L-systems.
Vittoria Rezzonico grows fractal broccoli and Sierpinski pyramids.
Menger
Cubes, Peter C. Miller.
Including some animated ray traces and a discussion of eliminating
irrelevant internal surfaces prior to rendering.
Menger sponge
floating in space. Everyone and his brother makes ray-traced
fractals with unlikely backgrounds nowadays, but Cliff Pickover was
there first.
Paperforms.
John Vonachen uses laser cutters and spray paint to make and sell paper
models of polyhedra, stellated
polyhedra, polyhedral complexes, Sierpinski tetrahedra, etc.
Project
X. "a shape that is homogenized, saturated with equalities, inanely
geometric, yet also irresolvable, paradoxical, UNHEALTHY"
