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The simplest algebraic language, denoted D. If X is the alphabet {x,x^_}, then D is the set of words u of X which satisfy 1. |u|_x=|u|_(x^_), where |u|_x is the numbers of ...

A portion of the Mandelbrot set centered around 0.3+0i with size approximately 0.1+0.1i.

The fractal illustrated above.

Fatou dust is a Fatou set for a point outside the underlying set. Such a set has zero area and has an infinite number of disconnected components.

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 ...

The Goffinet dragon is the fractal obtained by plotting all points spanned by powers of the complex number p=0.65-0.3i (Trott 2004, p. 9).

A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...

The H-fractal is a fractal constructed by starting with the line segments corresponding to a capital letter H, then iteratively placing smaller H's centered at the top and ...

The branch of algebraic topology which deals with homotopy groups. Homotopy methods can be used to solve systems of polynomials by embedding the polynomials in a family of ...

The term "ice fractal" refers to a fractal (square, triangle, etc.) that is based on a simple generating motif. The above plots show the ice triangle, antitriangle, square, ...