## Paratime

If you consider a cellular automaton of the one-dimensional variety it needs a line of pixels to see a pattern if you consider a 100 by 100 grid pattern of the output of the cellular automata and could there be a rule that would generate the same pattern but rotated by 90° this must correspond to an idea of par

Rudy Rucker speculated that there might be something called paratime, it works as follows…

States of a universe in time develop linearly, from start to end, with causes influencing the next frame of the movie so that each frame depends deterministically upon the previous. Let’s say you might assume a big bang, with increasing size, then maybe a contraction and eventual big crunch.

What if in some other perpendicular direction there was another development process where structures developed deterministically also, with more complexity building up as the paratime ticked away. I’ve done a very poor diagram below.

How could this be investigated ? it seems very hard but maybe there is a simulation that could be tried.

Consider a one dimensional cellular automaton which has a rule where one line of pixels generates a new line of pixels moving down the screen. the system starts with a random line of pixels and each new pixel in the next line is coloured black or white depending on the state of the three pixels above it. starting with a given pattern the output moves down the screen and generates a pattern like the one below with the triangles.

The neatest way to summarize a simple rule is shown in this last diagram.

If we consider these patterns to be tiny universes developing in time deterministically, each from a given set of starting conditions, then maybe some insight can be had into paratime if we ask:

is there a pair of CA Rules + Starting lines that generate the same pattern but one is a 90 degree rotation of the other ? If such a pair can be found then there are two deterministic “laws of CA physics” that generate the same pattern, with each direction of developing structure at right angles to the other. this is paratime.

I would like to code it and put it on a machine to run for a long while and see if it found anything.

In a cellular automata and to generate a pattern one needs a rule and a set of starting conditions if the rule is analogous to the laws of physics then the starting conditions must define the starting physical constants.

If you consider a cellular automaton of the one-dimensional variety it needs a line of pixels to see a pattern if you consider a 100 by 100 grid pattern of the output of the cellular automata and could there be a rule that would generate the same pattern but rotated by 90° this must correspond to an idea of paratime.

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