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The Feigenbaum constant delta is a universal constant for functions approaching chaos via period doubling. It was discovered by Feigenbaum in 1975 (Feigenbaum 1979) while ...

Consider an arbitrary one-dimensional map x_(n+1)=F(x_n) (1) (with implicit parameter r) at the onset of chaos. After a suitable rescaling, the Feigenbaum function ...

A curious approximation to the Feigenbaum constant delta is given by pi+tan^(-1)(e^pi)=4.669201932..., (1) where e^pi is Gelfond's constant, which is good to 6 digits to the ...

The Schwarzian derivative is defined by D_(Schwarzian)=(f^(''')(x))/(f^'(x))-3/2[(f^('')(x))/(f^'(x))]^2. The Feigenbaum constant is universal for one-dimensional maps if its ...

Nice approximations for the golden ratio phi are given by phi approx sqrt((5pi)/6) (1) approx (7pi)/(5e), (2) the last of which is due to W. van Doorn (pers. comm., Jul. 18, ...

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 biharmonic operator, also known as the bilaplacian, is the differential operator defined by del ^4=(del ^2)^2, where del ^2 is the Laplacian. In n-dimensional space, del ...

Given a Euclidean n-space, H_n=n+1.

If a polynomial P(x) is divided by (x-r), then the remainder is a constant given by P(r).

An object is amphichiral (also called reflexible) if it is superposable with its mirror image (i.e., its image in a plane mirror).