POV-Ray : Newsgroups : povray.advanced-users : Making Patterns with functions : Making Patterns with functions Server Time30 May 2024 09:54:06 EDT (-0400)
 Making Patterns with functions
 From: Bald Eagle Date: 5 Jan 2024 16:55:00 Message:
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Over the last 2 days, I've fallen down the mathematical pattern rabbit hole, and
have been experimenting with all manner of what can be done with a simple
pigment {function {}}
statement.

I currently have a list of 155 different patterns, including simple y = f(x)
style functions, implicit equations (some combination of x&y) = (some other
combination of x&y), and even some parametric polar equations and what I believe
are parametric Cartesian equations.

Hammering out that many equations one after the other and using different
methods to visualize the "raw" results has allowed me to learn some new things
and gain valuable insights into how best achieve a good, aesthetically pleasing
result, and why some patterns might be difficult to implement in the absence of
various "tricks".

At this junction, I would like to thank everyone in the POV-Ray community, and
especially Tor Olav Kristensen, Sam Benge, jr, William Pokorny, Jerome Grimbert,
as well as the vast Shadertoy community - most notably Inigo Quilez, Martijn
Steinrucken, and FabriceNeyret2, for inspiring me, and setting me on the path of
discovery with regard to using functions to make amazing patterns.

With that, I'll just leave here a most amazing Greek frieze pattern, produced by
an astonishingly small amount of code, adapted to SDL from a shader by
FabriceNeyret2.

While this is probably one of the most complex patterns I've adapted, simply due
to some specialized and highly technical methods that make its visibility even
possible, I'd love to see people experimenting with simple equations to produce
interesting patterns that we can build a library of.

After progressively trimming down the amount of code I need to make a simple
grid on a plane, I'd love to see such patterns code-golfed down to the bare
minimum, and then parameterized to increase their variation and versatility.

Happy New Year, everyone.

- Bald Eagle
```

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