# Fractal Recipes for Programmable Matter, Did Carol Marcus know the Recipe?

Does the generation of set resolution fractal objects offer an insight as to how future programmable matter may be manipulated? Once again Star Trek may have foreshadowed what may be coming.

# Iterated Function Systems

In a previous article examining the possible relationship between programmable matter as described in Star Trek: Discovery and the underlying nature of spacetime as a continually rewriting hypergraph structure I volunteered that it reminded me of iterated function systems (IFS) as method of constructing fractal objects.

Briefly, and loosely with the mathematical definitions so we don’t get too bogged down, IFS are a method of constructing fractal objects using a set of contraction mappings on a complete metric space¹.

It’s iterated as the set of functions is applied iteratively — simply supplying a point, letting the transformation move it, and using the resultant point as the start for the next iteration. Think like a feedback loop.

If the set of functions is contractive then there is a unique fixed point where the result of the calculated contractions will ultimately converge. This is referred to as the attractor. Interestingly this happens with any number of dimensions, but more…