Building arbitrary Life patterns in 15 gliders

It's not impossible that we could come up with a way of crashing less than 15 moving objects together to get an alternate RCT pattern.

Gliders are generally considered to be the "lowest common denominator", though, so adding complexity by allowing more types of spaceships isn't usually seen as an improvement.

... It also becomes possible to cheat: I suspect we could put together something like an "RCT8" if we allowed Corderships as well as gliders in the list of allowed moving objects that we start with. (2-engine Corderships' "engines" are switch engines, and we have to build four switch engines to get the RCT reaction started. Could probably just shoot down the extra switch engine with one glider, and go from there.)

How nonlocal are the entanglements in Conway's game of cellular automata, if they're entanglements with symmetry; conservation but emergence? TIL about the effect of two Hadamard gates upon a zero.

Quantum discord: https://en.wikipedia.org/wiki/Quantum_discord :

> In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement.

From "Convolution Is Fancy Multiplication" https://news.ycombinator.com/item?id=25194658 :

> FWIW, (bounded) Conway's Game of Life can be efficiently implemented as a convolution of the board state: https://gist.github.com/mikelane/89c580b7764f04cf73b32bf4e94...

Conway's Game is a 2D convolution; without complex phase or constructive superposition.

Convolution theorem: https://en.wikipedia.org/wiki/Convolution_theorem :

> In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms.

From Quantum Fourier transform: https://en.wikipedia.org/wiki/Quantum_Fourier_transform :

> The quantum Fourier transform can be performed efficiently on a quantum computer with a decomposition into the product of simpler unitary matrices. The discrete Fourier transform on 2^{n} amplitudes can be implemented as a quantum circuit consisting of only O(n^2) Hadamard gates and controlled phase shift gates, where n is the number of qubits.[2] This can be compared with the classical discrete Fourier transform, which takes O(n*(2^n)) gates (where n is the number of bits), which is exponentially more than O(n^2).

(Not just any such pattern, though -- a still life also means that it doesn't change when you evolve it according to Life rules.)

Definitely! It's hard to summarize that insight in any kind of concise way, though ... The Game of Life universe seems a bit too "fragile" to allow for the kind of emergent complexity that real-world physics supports. We can build self-constructing things like the https://conwaylife.com/wiki/0E0P_metacell , but if anything gets slightly out of place, the usual result is a truly horrific catastrophic explosion.

Conway's Life design work is kind of like building robots out of masses of subcritical uranium. Everything's fine until two robots unexpectedly bump into each other... which means you have to start out with everything very carefully balanced, such that that never happens.

So I guess one fairly obvious insight is that real-world physics supports more reliable and less explosive low-level structures than Conway's Life does, and those low-level structures can then safely be used as the basis for new levels of organization -- atoms -> molecules -> DNA -> bacteria -> eukaryotic cells -> multicellular organisms -> colonies of organisms -> ecosystems.

It's not clear how those higher levels of organization would work in Conway's Life. If they're possible, then they seem to be far beyond our current ability to simulate them -- though there's some recent research vaguely along these lines, about self-replicators that might be able to exert some control over the space around them:

https://conwaylife.com/forums/viewtopic.php?f=2&t=5364

I wonder if you could bypass this with a level of indirection.

If the GoL wizards can construct an expanding and initially configurable 'GoL in GoL' grid [1], they could configure the 'garden of eden' as the initial configuration for their 'GoL in GoL' simulation.

It's not the same thing, of course, but it would allow you to run Garden of Eden patterns still starting with just your initial 15 gliders.

To construct a garden of eden pattern, you must first construct the universe :)

[1] similar to https://www.youtube.com/watch?v=xP5-iIeKXE8