WEBVTT 00:00.060 --> 00:00.660 Hello again! 00:01.110 --> 00:04.710 In this video, we are going to start looking at Conway's Game of Life. 00:05.950 --> 00:10.510 This was devised by the British mathematician, John Conway, in 1970. 00:11.290 --> 00:16.690 He was interested in the field of "cellular automata", which was just starting at that point. 00:17.410 --> 00:22.240 He wanted to find a set of rules which would give interesting and unpredictable results. 00:22.930 --> 00:24.700 And he certainly succeeded with that! 00:25.900 --> 00:31.420 His work was picked up by a journalist called Martin Gardner, who had a column in Scientific American 00:31.420 --> 00:31.960 magazine. 00:32.590 --> 00:36.280 And it became very popular with mathematicians and computer programmers. 00:39.170 --> 00:41.510 What is a cellular automaton? 00:42.320 --> 00:46.250 This is something which emerged from research into how crystals grow. 00:47.240 --> 00:50.090 A cellular automaton is a grid of cells. 00:50.780 --> 00:55.160 The cells on this grid have two states, so "on" and "off", if you like. 00:55.760 --> 01:02.030 And the bit which makes it interesting, is that the state of a cell depends on the state of the 01:02.030 --> 01:03.260 cells around it. 01:03.920 --> 01:08.390 So this allows you to model systems which have interaction and feedback. 01:09.980 --> 01:13.730 So this can be used to model a lot of naturally occurring processes. 01:14.210 --> 01:17.480 For example, the patterns which appear on seashells. 01:18.140 --> 01:19.580 The way that plants respire. 01:20.060 --> 01:23.750 In Physics you can use its for phase transitions, and so on. 01:24.920 --> 01:29.960 A cellular automaton is "Turing-complete", which means that, in principle, you can use it to solve 01:29.960 --> 01:31.190 any computational problem. 01:31.730 --> 01:35.660 So there has been talk about using it for cryptography and neural networks. 01:37.460 --> 01:42.890 More philosophically, a cellular automaton is an example of a so-called "emergent" system. 01:43.250 --> 01:47.840 So this means basically a system where the whole is greater than the sum of the parts. 01:48.500 --> 01:50.390 For example, the human brain. 01:51.110 --> 01:57.380 This is just a load of molecules which are experiencing chemical reactions, but that can produce thoughts, 01:57.380 --> 01:59.330 feelings, consciousness and so on. 02:00.440 --> 02:03.410 It is also an example of a "self-organizing" system. 02:03.890 --> 02:10.100 This is where you have a system where, originally, all the components are arranged at random, and they organize 02:10.100 --> 02:13.520 themselves and set up a stable and robust arrangement. 02:14.090 --> 02:18.590 For example, if you have a bar of iron, all the atoms are going to be pointing in different directions. 02:18.980 --> 02:24.950 But if you bring a magnet up against this bar of iron, then the atoms are going to eventually all end 02:24.950 --> 02:28.070 up pointing in the same direction, and the bar will be magnetized. 02:30.520 --> 02:34.540 The Game of Life is played on an infinite two-dimensional grid of cells. 02:35.050 --> 02:37.610 Each cell on the grid is either "alive" or "dead". 02:38.060 --> 02:40.630 Or, if you prefer, "populated" or "unpopulated". 02:41.680 --> 02:43.740 The game is played by the computer. 02:43.750 --> 02:46.540 So I suppose, strictly speaking, it is really a simulation. 02:48.620 --> 02:50.420 In the game, or simulation, 02:50.990 --> 02:57.680 the grid goes through a series of generations, so the cells on the grid will become alive, remain 02:57.680 --> 03:04.970 alive or die out as the game progresses. So a live cell can survive to the next generation or die out. 03:05.600 --> 03:10.220 If we have a cell which is unpopulated in this generation, it may become populated in the next 03:10.220 --> 03:10.790 generation. 03:11.750 --> 03:17.300 And the fate of a cell depends not only on its own state, but also on the state of its neighbours. 03:19.270 --> 03:21.580 So these are the rules that Conway came up with. 03:22.000 --> 03:27.820 If we have a cell, which is live in this generation, and it has fewer than two live neighbours or more 03:27.820 --> 03:31.150 than three live neighbours, then it will die out in the next generation. 03:31.690 --> 03:36.670 So it will only survive if it has exactly two or exactly three neighbours which are live. 03:37.240 --> 03:42.640 If we have a cell which is unpopulated in this generation, it will become populated next time, 03:42.970 --> 03:45.340 if it has exactly three live neighbours. 03:45.970 --> 03:47.890 Otherwise it will remain unpopulated. 03:49.560 --> 03:50.850 So let's look at some pictures. 03:51.240 --> 03:52.590 Here is a cell. 03:53.190 --> 03:58.590 Each of the cells on the grid will have each neighbours, one on each side, one above and below, 03:59.040 --> 04:00.570 and four diagonally. 04:02.460 --> 04:08.640 If we have a cell, which is live, then it needs to have two or three neighbours which are live, in order 04:08.640 --> 04:10.410 to survive to the next generation. 04:11.130 --> 04:14.550 If it has one or less, or four or more, then it will die out. 04:17.260 --> 04:23.560 If we have a cell which is unpopulated, it needs to have exactly three live neighbours to become populated 04:23.560 --> 04:24.760 in the next generation. 04:25.240 --> 04:27.730 Otherwise, it will remain unpopulated. 04:28.950 --> 04:29.250 Okay. 04:29.250 --> 04:30.300 So that is it for this video. 04:30.750 --> 04:35.040 In the next video will look at implementing this, but until then, keep coding!