Tricky Decompositions

This fractal is an instructive example for people who have seen the gasket and a few of its relatives.

The primacy of the gasket in early examples of fractals makes this shape one of the easiest to recognize.

The most common response to first seeing this picture is, "It's half a gasket."

But we don't have rules for making half of a fractal.

The main lesson here is that we're looking for scaled copies of the whole shape, and the whole shape is not a gasket.

Tracing small copies of the outline of the whole shape, perhaps cutting them out of paper, is a good way to build up intuition for this process. Here's a decomposition.

In the x-direction we see the familiar Cantor middle thirds set; in the y-direction just a line segment.

Again, look for scaled copies of the whole shape. Here's a decomposition.

Return to Inverse Problems.