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A 4-state two-dimensional Turing machine invented in the 1980s. The ant starts out on a grid containing black and white cells, and then follows the following set of rules. 1. ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

Macdonald's plane partition conjecture proposes a formula for the number of cyclically symmetric plane partitions (CSPPs) of a given integer whose Ferrers diagrams fit inside ...

A function that arises in performance analysis of partially coherent, differentially coherent, and noncoherent communications. The generalized Marcum Q-function is defined by ...

Inspired by computer simulations of fossilized worms trails published by Raup and Seilacher (1969), computer scientist Mike Paterson at the University of Warwick and ...

The pentaflake is a fractal with 5-fold symmetry. As illustrated above, five pentagons can be arranged around an identical pentagon to form the first iteration of the ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

The Zernike polynomials are a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils. The odd and even ...

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these ...

The region lying between two concentric circles. The area of the annulus formed by two circles of radii a and b (with a>b) is A_(annulus)=pi(a^2-b^2). The annulus is ...