The Computational Beauty of Nature
Computer Explorations of Fractals, Chaos,
Complex Systems, and Adaptation

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Glossary - L

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Lamarckism     A method of heredity that does not apply to genetics but is applicable to social adaptation. Lamarckism posits that acquired traits can be passed from parent to offspring.

Lambda Calculus     A model of computation that is capable of universal computation. The Lisp programming language was inspired by Lambda calculus.

Learning     A process of adaptation by which synapses, weights of neural network's, classifier strengths, or some other set of adjustable parameters is automatically modified so that some objective is more readily achieved. The backpropagation and bucket brigade algorithms are two types of learning procedures.

LIFE     See Conway's Game of Life.

Limit Cycle     A periodic cycle in a dynamical system such that previous states are returned to repeatedly.

Linear     Having only a multiplicative factor. If f(x) is a linear function, then f(a+b) = f(a) + f(b) and c f(x) = f(cx) must both be true for all values of a, b, c, and x. Most things in nature are nonlinear.

Linearly (In)separable     Two classes of points are linearly separable if a linear function exists such that one class of points resides on one side of the hyperplane (defined by the linear function), and all points in the other class are on the other side. The XOR mapping defines two sets of points that are linearly inseparable.

Lisp     A programming language designed to manipulate lists that was inspired by Lambda Calculus and was the inspiration for Stutter.

Local Minimum (Maximum)     The bottom of a valley or the top of a peak; a point in a search space such that all nearby points are either higher (for a minimum) or lower (for a maximum). In a continuous search space, local minima and maxima have a 0 gradient vector. Note that this particular valley (or peak) may not necessarily be the lowest (or highest) location in the space, which is referred to as the global minimum (maximum).

Logistic Map     The simplest chaotic system that works in discrete time and is defined by the map x(t) = 4r x(t) (1-x(t)). Feigenbaum's constant was first identified for this map.

Lorenz System     A system of three differential equations that was the first concrete example of chaos and a strange attractor.

Lotka-Volterra System     A two-species predator-prey system that in its simplest form can display only fixed points or limit cycles. More complicated versions with three or more species can yield chaos.

L-System     A method of constructing a fractal that is also a model for plant growth. L-systems use an axiom as a starting string and iteratively apply a set of parallel string substitution rules to yield one long string that can be used as instructions for drawing the fractal. One method of interpreting the resulting string is as an instruction to a turtle graphics plotter. Many fractals, including the Cantor set, Koch curve, and Peano curve, can be expressed as an L-system.

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Copyright © Gary William Flake, 1998-2002. All Rights Reserved. Last modified: 30 Nov 2002