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Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...

A Julia set with c=-0.123+0.745i, also known as the dragon fractal.

The fractal J(-3/4,0), where J is the Julia set. It slightly resembles the Mandelbrot set.

A Julia set with c=-0.390541-0.586788i. The fractal somewhat resembles the better known Mandelbrot set.

A Julia set J consisting of a set of isolated points which is formed by taking a point outside an underlying set M (e.g., the Mandelbrot set). If the point is outside but ...

A Julia set with constant c chosen at the boundary of the Mandelbrot set (Branner 1989; Dufner et al. 1998, p. 225). The image above was computed using c=i.

A Julia set fractal obtained by iterating the function z_(n+1)=c(z_n-sgn(R[z_n])), where sgn(x) is the sign function and R[z] is the real part of z. The plot above sets ...

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

A recurrence equation (also called a difference equation) is the discrete analog of a differential equation. A difference equation involves an integer function f(n) in a form ...

A mathematical object upon which an operator acts. For example, in the expression 1×2, the multiplication operator acts upon the operands 1 and 2.