Adding dimensions to Conway's Game of Life

so if we consider a universe with only one spatial dimension we are going to see that it's only possible to have neighbors on our left side or on our right side so maximum of two neighbors and if we expand that universe to be two dimensional we will see that it's possible to have maximum of eight neighbors because now we can also have neighbors on top of us and below us and furthermore we can have diagonal neighbors on a two-dimensional universe going further if we expand to three dimensions it's possible to have up to 26 neighbors and we can see that the relation between this maximum number is three times the previous universe plus two and this is easy to understand because we can all always have the same neighbors as we did also on one additional direction so between one and two dimensional neighbors we have have added the dimension up and down and furthermore we can be neighbors with the one cell which was previously on our spot so that is the plus two in the formula now if we expand further to four dimensions we can have up to 80 neighbors in 5d 240 two neighbors and finally in 6d we can have 728 neighbors so that's already quite a lot of neighbors and here you are seeing a game of life simulation of just that 6d universe with up to 728 neighbors and we can see when we simulate this kind of universes that the possibilities of life are rapidly expanding as we add these dimensions but it's not always easy to live in such multi-dimension dimensional universes because if we use some simple rule for life here and we see the simulation go what usually happens is that it's very easy to expand in a multi-dimensional universe but if the space for expansion runs out it's very possible that the simulation is just going to die out and this is because the expanding universe no longer has any possibilities for life because the expansion is the only way to survive but here we are actually having a universe which is viable for life and even if there's no room for expansion this universe would stay alive if we look at the rules we have so that cells with one neighbors three neighbors six neighbors and finally nine neighbors are getting born in the six dimensional game of life universe and we can even remove some of these rules first we remove the one neighbor rule and we will see that some possibilities for life will disappear this universe is going to lose a flavor so to speak and some parts of the expanding universe are going to be darker because it's no longer possible to survive with only one neighbors and this is also going to have a big effect for the expansion of the universe because this rule cells with one neighbors getting born is very good for rapid expansion because diagonally you are easily going to have one neighbor and then you can just expand outwards and as i said before this is a kind of rule which is good for expanding but it can easily die out if the space for expanding runs out you can now see that on the borders of the universe there's more darkness and maybe the universe is not expanding as rapidly let's remove another possibility for life and now only cells with six or nine neighbors are going to get born and we will see that there is going to be even more darkness in the universe as another way of life becomes impossible and i can already say that this universe is going to survive because the number six is quite good for a six-dimensional universe when we study universes of different spatial dimensional count you will see that there are some key numbers which are very good for life in such universes and it also depends on the number what kind of behavior you are going to see in the universe for example in a three-dimensional universe the number four is very good for movement-like actions and if we expand to a 4d universe the number eight is going to be good for a movement like action because in some ways the number eight funny green face here right by the way in some ways the number four and eight are similar in corresponding to three-dimensional and four-dimensional simulations for reasons it's a little bit hard to go in such a short video but this is the case trust me on this maybe i will make a video about that in the future and if we expand that one might think that maybe in a five dimensional universe the number 12 or maybe 16 would be similar but at some point this kind of logic usually breaks because there's going to also be another kind of behavior which emerges in the more dimensional universe we have created now finally let's also remove the number six from this universe and now i can already say that this universe is a dying universe but it will be able to survive for a while because the number nine is imprinted in some ways in the universe and it's going to have possibilities for life with this number for a while but it's not going to be sustaining because the number nine is not going to be able to sustain sustain the life for very long because now the universe which was created on the previous step no longer has many means for life because the number nine is simply not enough to sustain life here now we have a decision to make whether we let this universe die or will we save it and i think this is pretty nice looking universe so i'm not going to let it die but instead i'm going to give it another chance with a number let's say number four i'm not sure if this is going to work though because number 4 and number 9 may not bear enough relation with each other to survive but let's give it a go now the next step of the universe what it's going to look like it seems like it's completely dark so the beautiful universe actually died out that's a shame but well sometimes this happens in life if you don't understand the universe you might just kill it if you don't tweak it correctly well happily we don't have such powers yet but this is all for this video i hope you enjoyed it and bye

Channel: Creetah

Views: 14,609

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Id: zUGKHWmOrpE

Length: 8min 17sec (497 seconds)

Published: Sun May 09 2021