f(x) = ln(5x^3 + 3x^2 + 7x + 1)

Back

Each pixel represents a starting value for Newton's iteration.  If after 20 iterations, Newton's Method has not located a zero of f(x), then the pixel is colored black.  All the brown pixels correspond to starting values that converge to the same root.  All the light green pixels correspond to starting values that converge to a different root, and so on.  Notice that there are exactly 3 different roots to which Newton's Method converges.  Real values between -4 and 4 and imaginary values between -5 and 5 are shown.  This fractal was created by David Hotchkiss in May 2004.

Back