1. Romanesco broccoli pattern 2D shader

    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:

    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

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

    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.

    golden = PI*(3-sqrt(5));
    To draw a secondary florets or a circle on polar coordinates we can use polar translation equations

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

    Updated 08-26-2013 at 05:13 AM by Artur