I think the coolest thing about this is the way time works. One step at each level is computed using a large number of steps at the level below. So as you zoom out you are sinking into an exponential vortex where each step takes days, years, millennia to change.
But ingeniously, the simulator smoothly scales its speed as you zoom, totally erasing the fact of time. I wish there was an indicator somewhere of how much game time was going by per real-life second.
EDIT: ...but in order to do that you'd have to declare one of the levels to be the "bottom" level, the one that runs in real time, and that would ruin the fractalness of it all...
The hows-it-done article describes the meta-pixel pattern concept then gives you the "clock-ratio" of the periodicity:
> In addition, the pattern has a period of 35328, so advancing 35328 generations will cause the generation at the meta level to advance by 1.
I would even say this time dilation is necessary because the pattern's self-similarity is across time, and if the two levels operate at different clocks, you need to slow down the next level as it comes up to the self-similar animated view of the prior level.
In other words, the structure at level n requires 35328 iterations of the self-similar structure at level n+1, so if you're bringing n+1 up to the self-similar view of n, you need to slow down n+1 as it's coming up to also hit the time-based self-similarity.
I wonder then if there's something like a time-invariant constant, maybe along the lines of the "computational complexity" of any view remains constant across all levels of zoom.
For some reason what really sticks out to me is how when you zoom out, you always come out of a different part of the circuit, so it doesn't feel like the normal repetitive fractal, you're seeing all the parts of the machine from different chronological angles or something.
Interestingly, the author's blog post [1] mentions that this is due to technical limitations and not specifically done by choice, although I do like the effect.
> When we zoom in, we discard the information of the largest meta-metapixel, so it is not always possible to reconstruct the same scene when we zoom out again.
> Since zooming in and out can be continued indefinitely, we also realize that we need infinite information to accurately represent "our current position".
"Another thing I know about screens is, you can go into them as far as you want forever. And you can come out of them too, but you might not end up in the same place that you started. You might get lost. Or you might not."
Imagination is fun. I'm pretty sure I can make your brain break a little bit more. Imagine they're all looped and there is no bottom level fastest super infinite computer.
Since the grid is infinite, it should be possible for one level to to be completely identical in its history to the next level. Thus you could identify all levels with each other to really be the same level. Then both space and time are circular in their scale. (The now-single level could nevertheless still be non-repeating both in space and time!)
Note that this is also how our own world works. Typical time scales of processes get faster as the length scales shorten. Somehow it feels inevitable for a dynamic multiscale structure.
armchair physicist moment: isn't this a straightforward outcome of c as a global "speed limit"? effects can't propagate faster than c, so I would expect that interaction "latency" decreases linearly with scale.
My read on the author's explanation story is he did actually solve the "consistency with time" and "consistency in position" problems that would make it a "rounds up to real-looking" at some zoom seam.
It's not cheating, but the trick is it's pre-computed.
Basically the structural patterns repeat, and you can pre-compute the patterns (which are also the sub-patterns), then basically tile the configurations and their transitions "across time". A naiive approach takes a few TB to store it all, but there's some clever optimizations that can bring it down. Finally once a "solution" through the tiling space was found, the author encoded it into a 4 mb png and built a display with some clever shaders.
I'm not saying it isn't technically impressive and super cool - but he clearly can't actually be computing infinitely recursive levels of GoL, so in that sense it's an illusion.
Pardon my poor vocabulary to describe the following:
But if the patterns are precomputed at whatever timescales, the patterns repeat in a predicable interval, based on the scale of time..
So, I wonder what each layer of pattern looks at from a perspective of a prime or true prime number scale digit...
Like if real-time baseline is 1 - and if you look at the pattern in a still frame at position scale 1. What is the pattern look like at time scale of the primes and true primes?
Whereas the primes and true primes are known discretes, so one could think of them as discrete dimensions of timescale based on the pattern represented at timescale position 1 (real-time)
And what if timescale at position 1 is some reflection of the pattern at the primes and true prime timescales... (assuming a dimension simply means the rate at which times flow at that energy level)
But ingeniously, the simulator smoothly scales its speed as you zoom, totally erasing the fact of time. I wish there was an indicator somewhere of how much game time was going by per real-life second.
EDIT: ...but in order to do that you'd have to declare one of the levels to be the "bottom" level, the one that runs in real time, and that would ruin the fractalness of it all...