4 ms·
Do we have any idea / intuition about what proportion of patterns are build-able? If not on an infinite grid, then some subset (i.e. 100% of 1x1 patterns are b
by NeoTar 4y ago
Do we have any idea / intuition about what proportion of patterns are build-able?
If not on an infinite grid, then some subset (i.e. 100% of 1x1 patterns are build-able, 80% of 3x3 patterns, 60% of 5x5 patterns, etc.)
- biggiemac42 4y agoThis is a really good and not at all easy to answer question. The most I can say is that folks earlier this year used some SAT solver equivalent to find notable patterns that cannot be constructed - including a still life and an oscillator https://conwaylife.com/wiki/Unsynthesizable_oscillator_1 https://conwaylife.com/wiki/Unsynthesizable_oscillator_1. This doesn't have much bearing on the probability of constructability for an arbitrary large pattern.
- JKCalhoun 4y agoYeah, I was wondering, with todays computing power, if it were possible to run outrageously large random Life universes and use some sort of software to look for "interesting patterns" (whatever that means). Or are these "discoveries" being done by hand?
- OscarCunningham 4y agoA lot of discoveries have come from 'soup search' where you start with a random 16 by 16 square and let it evolve. We've run over 156 trillion soups https://catagolue.hatsya.com/statistics https://catagolue.hatsya.com/statistics. This tends not no produce complicated machines, but rather small components that can then be engineered into larger patterns.
- chriswarbo 4y agoThere are "garden of eden" patterns which can only exist as an initial configuration: there is no pattern which evolves into a garden of eden, hence there can be no constructor capable of building them https://en.wikipedia.org/wiki/Garden_of_Eden_(cellular_automaton) https://en.wikipedia.org/wiki/Garden_of_Eden_(cellular_autom... If we limit ourselves to glider interactions, the article links to the following patterns which cannot be constructed (including garden of eden patterns): https://conwaylife.com/wiki/Category:Patterns_that_can_not_be_constructed_with_gliders https://conwaylife.com/wiki/Category:Patterns_that_can_not_b...
- knome 4y agoI 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 https://www.youtube.com/watch?v=xP5-iIeKXE8
- chriswarbo 4y agoSure, we can build them with "meta cells"; but that's just emulation (the same way a SNES emulator doesn't make my laptop a SNES). We already have GoL turing machines (with "tape factories" that travel faster than the read/write head); we could likewise use those to emulate GoL with arbitrary input, just by setting up an appropriate "tape". The result is far less pretty though ;) I touched on this in a sibling comment: https://news.ycombinator.com/item?id=33799084 https://news.ycombinator.com/item?id=33799084
- OscarCunningham 4y agoThere exists an 'orphan' pattern that cannot arise in any configuration after the first generation. When we look at large patterns, the proportion of them that contain an orphan tends to 1. On the other hand the smallest known orphan is 12 by 8, and we also know that all still lifes (unchanging patterns) with up to 21 cells can be built.
- enkid 4y ago21 cells would be a 3 by 7?
- OscarCunningham 4y agoGardens of Eden can be arbitrary patterns, whereas only the 21-cell still lifes are known to be constructible.
- enkid 4y agoOk, but what do you mean by a "still life" of 21 cells? Is that a rectangle in a larger field or is it an arbitrary set of cells?
- OscarCunningham 4y agoA pattern with 21 live cells in any bounding box.