Smooth 1D Colors #4

fractal 15

The sharp contrast in the color bands works best for two complementary colors. Black and white is probably the best choice. Today’s example feature a more gradual color change. From white, through some shades of brown and then shades of blue. The interior is set to the traditional black.

Back in the day, when fractals and personal computers were new, most color graphic cards had a 256 color table. Each pixel is assigned a color number from 0 to 255 in memory, which is used to look up a color in the table. 16.8 million total colors were possible, but only 256 could be displayed at any one time. That graphics design worked out well for fractal coloring which is basically paint-by-numbers. The original DOS fractal program, Fractint, had a feature that would rapidly change the color table in the graphics card which created a trippy psychedelic effect on the fractal.

Now (and for the last 20 years) computer monitors are capable of displaying all 16.8 million rgb colors.

The palette used in this picture is actually a mathematical formula that takes a (continuous) real number and directly generates a color in the 16.8 million color space.

Even if you define a palette as a list of discrete colors, then by using interpolation it is possible to generate a smooth transition between any two colors in the list. It makes sense to ask for color number 3.2, which would be a blend of 80% color 3, and 20% color 4.

So palettes are, or can easily be made into continuous functions that convert real numbers to colors. The discrete colors in this picture are due to the discrete nature of integer numbers, the escape count, and not due to any limitation in the color palette.

When palettes are defined as continuous functions, it is possible to scale palettes to speed up or slow down color transitions. For example instead of using color(x), one could use color(a*x) where a is a scale factor. The only difference between today’s picture and yesterday’s is a color scale factor of 1/3.

And now, a special addendum for those suffering with technical pedantry syndrome. Yes, 16777216 different colors is still a discrete set of colors. And yes if you look really hard you can see the difference between red #A00000 and red #A10000 which differs in red intensity by 1/256 of the full gamut. But for our purposes, our displays show a continuous range of colors.

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