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Description
I'll probably have vast improvements to this technique in the near future, but I wanted to share what I've been working on.

A lot of my old art was based on generating a sequence for each point in the image, and then analyzing that sequence using some mathematical techniques I had developed. I used pretty slapdash and arbitrary ways to generate sequences back then, though.

It occurred to me that, in an escape-time fractal like Mandelbrot, "generating a sequence for each point" is exactly what you're doing, by iteratively applying some non-linear recurrence relation ("escape time" is just the length of the sequence).

The colour at each point of this Mandelbrot figure is based on the coefficients of a linearization of the non-linear recurrence relation (zn = zn-12 + c) at that point.

Full view / download to see the most interesting detail.

Description
I'll probably have vast improvements to this technique in the near future, but I wanted to share what I've been working on.

A lot of my old art was based on generating a sequence for each point in the image, and then analyzing that sequence using some mathematical techniques I had developed. I used pretty slapdash and arbitrary ways to generate sequences back then, though.

It occurred to me that, in an escape-time fractal like Mandelbrot, "generating a sequence for each point" is exactly what you're doing, by iteratively applying some non-linear recurrence relation ("escape time" is just the length of the sequence).

The colour at each point of this Mandelbrot figure is based on the coefficients of a linearization of the non-linear recurrence relation (zn = zn-12 + c) at that point.

Full view / download to see the most interesting detail.