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Despite appearances to the contrary, the whole of the stalk (taken from the Mandelbrot) is 'coated' in the same bright white that the tip is at the top right...



In fact, the whole of the Mandelbrot is like that - zoom in far enough, and the edge is always the same colour. Is there a coloring algorithm so that different edges of the Mandelbrot have different colours? In the stalk example, I want the lower parts of the stalk to be more green.

Twinbee,

You need some way to characterize the different areas so you can color them differently. Off the top of my head, I'm thinking that you could use the average iteration value for a circular area around a point in question in order to color it. Areas deep in a "groove" are surrounded by high iteration pixels, even if you exclude neighbors that are Mandelbrot points. Areas that are out on the periphery of the set should be surrounded by pixels with lower average iteration values.

Unless you're writing your own fractal-rendering application I'm not sure how you'd accomplish this though.

I am writing my own fractal app, so I might give this a try. It occurs to me that averaging iteration values could produce smooth color transitions without the performance hit of using a continuous function (like distance estimates, continuous potential, fractional iterations values, etc) for coloring.*

Hmm....


Duncan


*My app uses a boundary following algorithm to skip iterating the interior of contiguous areas with the same iteration value. Some continuous functions like distance estimates are computationally expensive on their own, and others that aren't so bad still force me to iterate every pixel, so I lose the speedup of the boundary following optimization when I calculate.