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In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...

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 ...

A one-dimensional map whose increments are distributed according to a normal distribution. Let y(t-Deltat) and y(t+Deltat) be values, then their correlation is given by the ...

Although a numerically computed chaotic trajectory diverges exponentially from the true trajectory with the same initial coordinates, there exists an errorless trajectory ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...

A class of curve defined at integer values which hops from one value to another. Their name derives from the Greek word betaalphataurhoalphachiiotaomicronnu batrachion, which ...

The curlicue fractal is a figure obtained by the following procedure. Let s be an irrational number. Begin with a line segment of unit length, which makes an angle phi_0=0 to ...

The Haferman carpet is the beautiful fractal constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[1 1 1; 1 1 1; 1 1 1],1->[0 1 0; 1 0 1; ...

The Blancmange function, also called the Takagi fractal curve (Peitgen and Saupe 1988), is a pathological continuous function which is nowhere differentiable. Its name ...

A substitution system in which rules are used to operate on a string consisting of letters of a certain alphabet. String rewriting systems are also variously known as ...