Harmonic Divergence
Harmonic divergence is used to create smooth regular patterns. It's a nice tool for an abstract expressionist. "Kasimir Malevich", "Suprematism", "Evolution of Blue", "Relativism", "Smoky", all these paintings were created just with harmonic.
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Remarks
Definition of harmonic function starts with parameters of so-called affine transform.
It rotates the pattern around arbitrary "focus" point and shifts it by extent of horizontal and
vertical offset. There's common practice to use random numbers in place of affine parameters.
It varies a painting but doesn't change its style.
Harmonic pattern has a regular repeating design that reflects the values of period,
sub-period and distortion. Each of these parameters is spit on horizontal and vertical
parts. Disproportional pairs break the symmetry.
Saturation defines extent of the function peak. If it exceeds the limit an
overflow happens. Overflowing visually looks like a number of curved edges with sharp boundaries.
The next pictures show common use cases of harmonic function.
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| period = sub-period distortion = 0 |
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| period = sub-period distortion = 0.5 |
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| period = sub-period distortion = 2 |
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| period < sub-period distortion = 0 |
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| period < sub-period distortion = 2 |
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| period > sub-period distortion = 0.1 |
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| period > sub-period distortion = 0.6 |
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| period > sub-period distortion = 1.2 |
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| period > sub-period distortion = 1.8 |
Example
# Creates a randomly rotated # harmonic pattern Harmonic angle random[0:2pi] focus 0 0 offset 0 0 period 2 2 sub-period 10 10 distortion 5 5 saturation 1
...read about Fourier divergence