Perspex machine

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The perspex machine is a theoretical computer with a single instruction that performs a geometrical transformation and a jump. It has applications in computer vision systems for modelling optics.

The perspex machine is commonly simulated in terms of a perspex, short for "perspective simplex" which, in turn, is commonly represented as a 4 x 4 matrix ^[1] with column vectors x, y, z and t:

It is claimed that the perspex machine has various interesting properties, for example:

The perspex machine is deterministic.
Perspex programs are robust in the face of deleted or altered instructions.
A perspex program can be approximated (badly) by a single perspex instruction, and the approximation can be gradually improved by adding instructions until the original program is reconstructed.

The transformation is piecewise continuous, not discrete, which makes the theoretical perspex machine a hypercomputer. Consequently a digital computer cannot emulate the theoretical perspex machine, but it can simulate one approximately. The co-ordinates of the transformation are transreal numbers which means that the theoretical perspex machine, or a digital simulation of it, has no arithmetical exceptions.