Fractal Geometry

IFS with Memory - Sample

1-step memory

Can we build pairs of lines whose endpoints belong to 2-cycles? One approach is to guess the placement of the lines and allow those pairs of transitions corresponding to occupied length 2 addresses.

What happens if we try to combine some of these lines? The results can be more complicated than we might expect.

Examining some of these combinations of lines leads to the notion of romes, central to understanding which of these pictures can be made by IFS without memory (but with more transformations).

2-step memory

Can we use 2-step memory to build 16 gaskets in the unit square?

From the gaskets example, we see which 2-step memory configuration corresponds to a given 1-step memory configuration. From this we can recognize which 2-step memory IFS pictures cannot be generated by a 1-step memory IFS.

Return to IFS with Memory Lab.

1-step memory
	Can we build pairs of lines whose endpoints belong to 2-cycles? One approach is to guess the placement of the lines and allow those pairs of transitions corresponding to occupied length 2 addresses.
	What happens if we try to combine some of these lines? The results can be more complicated than we might expect.
	Examining some of these combinations of lines leads to the notion of romes, central to understanding which of these pictures can be made by IFS without memory (but with more transformations).
2-step memory
	Can we use 2-step memory to build 16 gaskets in the unit square?
	From the gaskets example, we see which 2-step memory configuration corresponds to a given 1-step memory configuration. From this we can recognize which 2-step memory IFS pictures cannot be generated by a 1-step memory IFS.