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The definition of an Anosov map is the same as for an Anosov diffeomorphism except that instead of being a diffeomorphism, it is a map. In particular, an Anosov map is a C^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 ...

The Cantor function F(x) is the continuous but not absolutely continuous function on [0,1] which may be defined as follows. First, express x in ternary. If the resulting ...

There are several versions of the Kaplan-Yorke conjecture, with many of the higher dimensional ones remaining unsettled. The original Kaplan-Yorke conjecture (Kaplan and ...

A New Kind of Science is a seminal work on simple programs by Stephen Wolfram. In 1980, Wolfram's studies found unexpected behavior in a collection of simple computer ...

There are several fractal curves associated with Sierpiński. The area for the first Sierpiński curve illustrated above (Sierpiński curve 1912) is A=1/3(7-4sqrt(2)). The curve ...

The Church-Turing thesis (formerly commonly known simply as Church's thesis) says that any real-world computation can be translated into an equivalent computation involving a ...

A fractal produced by iteration of the equation z_(n+1)=z_n^2 (mod m) which results in a Moiré-like pattern.

Computer algebra is a diffuse branch of mathematics done with computers that encompasses both computational algebra and analysis.

The covering of a plane curve with disks of radius epsilon whose centers lie on the curve.