I don't have an extensive mathematical background- what I do know I've learned outside of classrooms, although I did pick up a trick or two in various classes through the years. I know some basic manipulations of e, sin, and cos (series expansions of these, and various other series). Of course I'm familiar with complex numbers, trigonometry, and the various other forms of math I've used to write the various fractal formulas I've created.
A little calculus, when needed.
I'd prefer a quick and dirty mathematical explanation: a simple equation that I can see working, from which I can then learn the methods used to derive the equation. As I'm already familiar with the formulas, I'd like to think that the correct solution will "click", or make sense to me once I've seen it.
I'd simply like to see what relationship should be used for n=4,8,12, OR better yet, I'd like to have a continuous relationship so that n could be incremented smoothly, which I think would look really nice on certain fractals.
For now, we can greatly simplify it by reducing the problem to 2 dimensions.
theta= n * atan2 (x + iy)
temp_x = cos(theta)*magnitude
if (x< |y|) then temp_x = -temp_x
else if n==3,5,7,9....
if (x< 0 ) then temp_x = -temp_x
new_x = temp_x + x_pixel_value
new_y = sin(theta) * magnitude + y_pixel_value
Actually, we cannot see the discontinuities in 2d fractals... so... dunno. anyways, should proceed to something else for now.