This picture shows a Sierpinski carpet in `harmonic
coordinates'.
If h_1(x) is the harmonic

function
in the pictures above, and h_2 is its rotation by
90 degrees, this is the image of the SC

under the map which sends x to (h_1(x),h_2(x)).

The next two pictures show the heat kernel (or transition density of a random walk) on some Sierpinski carpets.