Newton-Raphson type Fractal


If your browser supported Java, You would see a nice fractal here.


This fractal is created by trying to solve the equation x3 = 1, using the Newton-Raphson method. This involves defining the function f(x) = x3 - 1, and using it in an iterative formula which should converge to zero, thus finding a value of x which is a solution to the first equation. This formula is:

xn+1 = xn - f(x) / f'(x)

Where f'(x) is the derivative of f(x).This fractal applies the formula to each point on the complex plain, and colours it according to how many iterations are required for f(x) to converge (approximately) to zero. In the fractal, the bottoms of the basins (boring regions of the fractal) are actually solutions of the origional equation.

Since this fractal doesn't have a julia set equivalent, I made the julia set of this fractal do the same type of fractal but on the equation x3 = c.


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