George Nees: Formel, Farbe, Form

Computerästhetik für Medien und Design
A German book from 1995

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The author used the following 8 base colors. They are manually ordered to look like a rainbow.

• #000
• #00f
• #0ff
• #0f0
• #ff0
• #f00
• #f0f
• #fff

The author continues to think of the pixels on the screen as a grid of larger 2 × 2 pixel cells. Each of the 4 pixels in one of these cells can have one of the 8 base colors. That's effectively some kind of dithering. In theory, there are 8^4 = 4096 possible combinations. The author excludes duplicates in a quite clever way, which leaves the following 330 colors.

This is not an image. You can look at the code.

Blur the dither pattern

Why 330? The idea is that the total number of possible combinations contains lots and lots of duplicates. For example, the combinations 1000, 0100, 0010, and 0001 are all the same: 3 parts of color number zero, and one part of color number 1. An iterative formula to calculate the number of unique combinations is a / n * (n + 7) where n is the number of pixels in a single cell and a is the number of colors from the previous iteration.

• Iteration 1: 8 possible combinations
• Iteration 2: 8 / 2 * (2 + 7) = 36
• Iteration 3: 36 / 3 * (3 + 7) = 120
• Iteration 4: 120 / 4 * (4 + 7) = 330

You can think of these numbers as

• The length of a line.
• The area of a square with one corner cut off, but the diagonal included where both pixels have the same color. As a formula: ((8^2 - 8) / 2) + 8
• The volume of a cube, but with so much cut off that only a single triangular corner remains. As a formula: ((8^3 - 8^2) / 4) + 8
• The volume of a 4-dimensional cube, again with all but one corner cut off.