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

Let (x_0x_1x_2...) be a sequence over a finite alphabet A (all the entries are elements of A). Define the block growth function B(n) of a sequence to be the number of ...

Due to nonlinearities in weather processes, a butterfly flapping its wings in Tahiti can, in theory, produce a tornado in Kansas. This strong dependence of outcomes on very ...

A fractal which can be constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[0 1 0; 1 1 1; 0 1 0],1->[1 1 1; 1 1 1; 1 1 1]}. (1) The size ...

A fractal-like structure is produced for x<0 by superposing plots of Carotid-Kundalini functions ck_n of different orders n. the region -1<x<0 is called fractal land by ...

The Cesàro fractal is a fractal also known as the torn square fractal. The base curves and motifs for the two fractals illustrated above are shown below. Starting with a unit ...

Determining the length of a country's coastline is not as simple as it first appears, as first considered by L. F. Richardson (1881-1953) and sometimes known as the ...

A set of orthogonal functions {phi_n(x)} is termed complete in the closed interval x in [a,b] if, for every piecewise continuous function f(x) in the interval, the minimum ...

The computational paradigm is a term introduced by Wolfram (2002, 2021) to describe the idea of using simple programs rather than mathematical equations (the latter of which ...