1.F. The Inverse Problem

Steps

Remarkably, solving the inverse problem has only two steps:

1. Using the self-similarity (or self-affinity) of F, decompose F as F = F₁ U ... U F_n, where each F_i is a scaled copy of F.

Because the transformations can involve rotations, reflections, and scalings by different factors in different directions, decomposition is not always as simple a task as it may seem at first.

Here are some examples of more complicated decompositions.

An additional problem is that decompositions never are unique.

Here are some examples of different decompositions of the same fractal.

2. For each piece F_i, find an affine transformation T_i for which T_i(F) = F_i. (By "find an affine transformation" we mean find the r, s, theta, phi, e, and f values.)

Return to the Inverse Problem.