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photo: Romanesco broccoli

I started playing with fractal shaders and in particularity I wanted to reproduce romanesco broccoli in SL. At first it was just a simple experiment but after each obstacle I got more persistent so eventually I discovered the world of calculus.
I'm going to skip the theory part about phyllotaxis, Fibonacci etc and get straight to the shader math. Good site that explains it all is: http://www.math.smith.edu/phyllo/

Most of the math was found on Wolfram and WikiPedia pages

First off we need to convert our UVs from cartesian to polar coordinate system

Code:

 r = sqrt( pow( x, 2 ) + pow( y, 2 ));

Code:

theta = atan( x, y) + PI;
// Note that PI offset has been added for polar translation 
// equation to work (for secondary florets)

Next, Golden Angle for distribution pattern.

Code:

golden = PI*(3-sqrt(5));

To draw a secondary florets or a circle on polar coordinates we can use polar translation equations

Code:

r2 = sqrt(r*r-2*r*r0*cos( theta-th0 )+r0*r0);

...

Updated 08-26-2013 at 06:13 AM by Artur

Tags: calculus, fractals, math, renderman, rsl

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