Art for maths sake

Sampling every 100, 50, 25, 10, 5, 1 steps.

This is the explanation for the images:

"First order of business was to fix my program from last post. Obviously the 22.8GB variable had to go. I managed to replace it with two 20KB variables, but in exchange for  that I have to spend a lot longer outputting. As per usual the program runs the entire simulation before outputting anything. When it gets to the visual output stage I have a counter which goes from 2 to 100000 with a step size of n. Every time the counter increments I change the colour of the cell that the ant is currently in to the colour it is meant to be at that turn according to the pre-processed simulation. That means that to get the full output I had to use a step size of 1, which is particularly processor-intensive but works. I then thought to myself "what would happen if I didn't use a step size of 1?". That resulted in the images above."

 I quite like the variety of styles in the images above, in particular:

• The sparsity of the 100-step image.
• The polka-dot of the 10-step image.
• The suspiciously like a colour-coded topological map 1-step image. (I wonder if I could alter Langton's Ant to produce a randomly generated landscape...)

If you have an opinion please comment below, I want to pursue these further and it would be great to have some idea of what looks best!

Oh and seeing as someone managed to solve my last number pattern (it was the differences of consecutive 5th powers) I have come up with a new one!

3,

mathmo

P.S. This is a bloody difficult one, I will be impressed if someone gets it!