Smooth 1D Colors #9

fractal 20

Here is another example of a low zoom fractal using Continuous_(smooth)_coloring. Wikipedia gives this method a name that is too generic. There are other smooth coloring methods. I am going to call this method the log-log color method. (The reason is obvious if you check the link.)

In earlier posts I used linear and nonlinear rescaling to tweak the colors on deep zoom fractals. Now, after applying the smooth color algorithm, palette rescaling can be used to tweak colors on low zoom fractals.

I am not going to demonstrate this continuous color method on a deep zoom fractal. Since this method is carefully crafted to match the escape count, up to a fractional amount there is no appreciable difference in the resulting images between the two methods.

I should also mention that the log-log method only works for degree-2 polynomials like z^2+c. It can be generalized to other polynomials, but often people overlook that. It does not generalize to non-polynomial formulas.

Tomorrow I will present a method that works everywhere.

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