Mandelbrot set (redirected from Mandelbrot sets)

Mandelbrot set [¦män·dəl‚bröt ‚set]

(mathematics)

The set of complex numbers,c, for which the sequences₀,s₁, … is bounded, wheres₀=0, ands_n+1=s_n²+c.

---

(mathematics, graphics)

Mandelbrot set - (After its discoverer, Benoit Mandelbrot) The set of all complex numbers c such that | z[N] | < 2 for arbitrarily large values of N, where z[0] = 0 z[n+1] = z[n]^2 + c The Mandelbrot set is usually displayed as an Argand diagram, giving each point a colour which depends on the largest N for which | z[N] | < 2, up to some maximum N which is used for the points in the set (for which N is infinite). These points are traditionally coloured black. The Mandelbrot set is the best known example of a fractal - it includes smaller versions of itself which can be explored to arbitrary levels of detail. The Fractal Microscope.