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

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Glossary - T

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Theorem     A statement in a formal system that has proof.

Theorization     A process by which scientists attempt to understand nature; it is the complement to experimentation. Theorization is the process of building mathematical models for how things work. Scientists always desire theories that are simpler than the data they explain. See also Occam's Razor and simulation.

Three Body Problem     The problem of determining the future positions and velocities of three gravitational bodies. The problem was proved unsolvable in the general case by Henri Poincaré, which forshadowed the importance of chaos. Although no analytical solutions are possible in the worst case, a numerical solution is sometimes sufficient for many tasks.

Threshold     A quantity added to (or subtracted from) the weighted sum of inputs into a neuron, which forms the neuron's net input. Intuitively, the net input (or bias) is proportional to the amount that the incoming neural activations must exceed in order for a neuron to fire.

Time Complexity     A function that describes the amount of time required for a program to run on a computer to perform a particular task. The function is parameterized by the length of the program's input. See also space complexity.

Time-Reversible     A property of dynamical systems that can be run unambiguously both forward and backward in time. The Hénon map, Lorenz system, and vant cellular automata are all time-reversible, while the logistic map, the Mackey-Glass system, and most other cellular automata are not. Time-reversible systems are described by functions that are invertible.

Time Series     A sequence of values generated from a dynamical system over time. Chaotic systems can be analyzed by examining the time series generated by a single portion of the system. See also embedding.

Tit-for-Tat     An effective strategy for playing the Iterated Prisoner's Dilemma. Tit-for-Tat starts by cooperating, and then does whatever its opponent did in the previous round of play.

Top-Down     A method of examining things that first looks at higher-level phenomena and then tries to explain lower-level patterns in terms of the higher-level observations. This is the exact opposite of bottom-up. See also holism and reductionism.

Transpose     An operation that flips a matrix about the main diagonal.

Turing Machine     A model of computation that uses an underlying finite-state automaton but also has an infinite tape to use as memory. Turing machines are capable of universal computation.

Turtle Graphics     A simple language for drawing graphics in which a ``turtle'' is used to make strokes on a plotting device. Typical commands include ``move forward,'' ``draw forward,'' and ``turn left.''

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