Monday, March 19, 2012

'Infinity Computer' Calculates Area Of Sierpinski Carpet Exactly - Technology Review

'Infinity Computer' Calculates Area Of Sierpinski Carpet Exactly - Technology Review  Sergeyev begins by adding a new axiom to the axiom of real numbers, which he calls the infinite unit axiom. This introduces grossone--the infinite unit.

Because it is governed by the other axioms of real numbers, grossone behaves much like one too. So it's possible to multiply grossone, divide it, add to it and subtract from it, just as is possible with other real numbers.

That suddenly makes working at infinity much easier by using a computing process that Sergeyev calls the infinity computer, which has the additional axiom built in. "The introduction of grossone gives a possibility to work with finite, infinite and infinitesimal quantities numerically," he says.

To show off its power, he works through the Sierpinski carpet examples given above, revealing how it's possible to keep track of the number of iterations at infinity simply by adding or subtracting real numbers from grossone. If a square can created in grossone steps, a square doughnut can be created in -grossone minus 1- steps. In this way, it's a simple matter to differentiate between any of the shapes in carpet sequence.

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