Infinitely large cellular automata on a small grid

[t686]

 

Goal: To use the parallel nature of a cellular automata and convert it to an infinite grid with infinite speed.  The idea is that a single long line (infinite) in B3/S12456 breaks up in space consistently while sweeping past the screen, it has to sweep past an infinite traveller that criss crosses through the grid outside the bounded area in an imaginary area that relies on the way cellular automata are.  All cellular atuomata fractally decrease in size so if you have large worm shapes at the start, they get smaller and smaller with no real change.  My idea is that by having a line sweep through, you can make an infinitely large grid of the same basic pattern repeated, but at the very start on the edge, since that original line breaks up, you'd put some leftover remnant pattern after it swept through something, and that determines what "is out there" in the infinite large region (and it doesn't necessarilly have to be symmetric out there), but you would rely on whatever remaining to affect a spinning oscillator from the start, and then have the spinning oscillator break up, by disintegrate along a stable path, like an unstable point that tips over but does so in a computing way.

You can see in the first post on the conway life forum: http://www.conwaylife.com/forums/viewtopic.php?f=11&t=3195&start=0

Starting from a central region 4 runners shoot down, the tip of the runners don't change and further and further from the tip there is slight changes.  That's similar to RedBarron's spinning wheel, in that during acceleration, a "first wave" flies off his wheel, and since it's accelerating, the wheel comes back and shoots an identical wave (with slight change) trailing right behind it.  Also, since his wheel are repeated mountains side by side, if he had a plane square rotating instead, the edge would come towards you and then away, but it travels in a circular path, but since his wheel is wavy (mountains side by side) the actual path of a particle travelling is not a circle but square shaped (and that's impossible with any other design including the plane square rotating, that's impossible to, so he made an impossibility).  So he has embedded a square grid in our circular world.

Now if you look at my pattern, you can bound the edges of a cellular automata, like pac man where something leaving one side enters the other.  I found that in a sphere edge wrapping in Golly (2d automata program), using that X shape pattern in the first post linked, in the bottom left and top right corners, you can split the center in such a way that a single diagonal is only in that bounded grid.  But the unique thing is that using that grid, the X, two diagonals are coming back and connecting to each other, but what's outside the grid (you can play with the X's on making connecting ones) you can make an infinitely large arrangement of the X's by having a broken line at the initial start right on the edge of the grid.  In that rule B3/S12456, a single long line travels in space and starts to break up fractally.  But it sweeps through the whole grid no matter how long at long line is.  But this is my idea.  Instead of using the parallel nature of the cellular automata, arrange the pattern so that remember I said a runner shoots through space and travels slowly.  You can arrange things so a runner shoots a virtual infinite distance in finite time in that it returns back to the bounded grid by setting things up properly.  If the long line I also mentions has to travel through the zig zagging line, that would determine what path and what happened, so you could in effect make like a domino computer that is not really infinite, because in a bounded grid there's a limit to the number of patterns but if you have say at the start 10,000 cells in the bounded grid, it would  be a repeat of the original bounded size of 10,000 cells, but 2 to the 10,000 of them, so it would be an enormous thing to travel through.  Also, if would be similar to a black hole in that the horizon an observor looking at the outside universe would see the entire universe occuring in a fraction of a second, so in this way what's outside the grid (by having a finite speed runner shooting some path, you remove the parallel aspect common to cellular automata, and convert it to a domino computer with infinite size and infinite speed.  I'm not sure if Redbarron's idea is key to making the pattern correct, but his implementation of embedding a square lattice in our circular space, tilts things, so you might have to arrange the initial pattern in a fractally increasing hexagonal arrangement (hexagonal is same as our circular space whereas square grids are not), but then you can remove the bound after the initial infinite speed-up and due to the unique arrangement, it will convert back to a square lattice, since you can make an initial hexagonal arrangement split up in a sphere bound, so half of the X's are on 4 of the edges, and when viewed from a sphere wrap they are hexagonal, but when you remove the wrap and let it expand, since they are split in half on the edges, you can't say they're hexgonal now and now they're square like RedBarron's device.  This also may not be unique to 2d but might be made with a simple 1d automata with the left and right side wrapped, and turning it into an infinitely long line that travels with the middle bounded area.

Also, in Golly you can layer or place two identical or different automatas side by side, so that due to the flickering pattern on the edge of both, you could infer that both must interfere with each other, and that might make it quantum, in that you would have to find something where the two are interacting in infinite space outside the grid due to the pixels on the screen nearby (in averaging the pixels of two patterns side-by-side they get smeared in the brightness), so you may be able to use that to generate an interaction in infinite space between two different but maybe similar bounded patterns, that then both expand and overlap each other (then you can use the theory of additive cellular automata if a pattern is deduced, you can then use the parallel nature of that to add the two patterns together).

Also, and here is the key, no matter how large the grid is, due to random chance, there is always something one one side interacting with another in some way (you can look at Wolfram's A New Kind of Science to see that), so straight lines are lightning bolt through the pattern (in the random flicker of this pattern) constantly even if it's infinite in size, so that may be used as well.

 

 

Edited September 4, 2018 by t686

[t686]

Also, I noticed on youtube of a video of an arduino cellular automata, since it's a video, a line sweeps down the screen and I noticed the pixels change as that line swept past the small Life patterns.  So recording the pattern, and seeing the effect of a swept line past patterns, you might deduce the remnant pattern of that original long line in the imaginary infinite space.  Also, you may have to use the shrinking automata rule after my exploding (shrinking: B35/S5678 or B36/S5678) so that usually when I use that shrinking rule or actually always, the shrinking rule leaves single tiny cells behind.  But if you make the long line remnant on the edge that's left over after deducing the remnant of the arrangement of the long line that's broken up, then maybe you can arrange things so in the infinite space, there is something different there that actually makes a bounce back in the bounded grid in the shrinking rule, so things shrink down, bounce back constantly.  And in the shrinking rule I remember not the explosive rule, a long line breaks up fractally.  But you'd have to use the explosive rule B3/S12456 first before applying the shrinking rule, then notice a bounce back.  Softology's blog of the fire automata is like a gas or hpp automata and his effect actually has shrinking down and bouncing back, but mine is completely deterministic, and with a hexagonal hpp automata that is completely probabilitic, so to make a quantum computer you have to have complete determinism as the underlying rule like this and getting nondeterminism of bouncing back from a shrink as a side effect.

[t686]

This is a picture of the patterns it makes:

This is an example of how automatas just fractally descrease in size: 

Edited September 5, 2018 by t686

[Ghideon]

9 hours ago, t686 said:

Goal: To use the parallel nature of a cellular automata and convert it to an infinite grid with infinite speed.

Ambitious, but infinite speed is not possible as far as I know.

9 hours ago, t686 said:

That's similar to RedBarron's spinning wheel

 Yes, the fact that it is never going to work as as means of delivering evidence of some unknown aspect of physics is strikingly similar.