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); ...

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)

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

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

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