Newton's fractal

characteristics:

created when using newton-rapson method to find roots of complex function
each pixel is represented as complex number and then colored according to which root it converges to

target:

let user define root count
display fractal and allow changing the polynomial function by shifting roots
make one iteration further when space is pressed

requirements:

roots -> coefficients -> derivative -> function
space translation
colors pallete

procedure:

get length of polynom from user
generate roots
find the coefficients and derivative
display the fractal with shiftable roots
when root is clicked on, shift it with mouse
when arrow is clicked on increase the number of iterations for the newtons method

model:

roots: Complex[]
colors pallete: Colors[]
camera: Camera

how to find coefficients:

go from 0..n
find unique combinations of n-i-1 roots (eg. [[C1, C2], [C2, C3], [C1, C3]])
multiply the inside (eg. [C1C2, C2C3, C1*C3])
sum them together (eg. C1C2+C2C3+C1*C3)