Researchers study these simpler systems in the hope that they will shed light on the more complicated real-world phenomena. However, many real world systems such as the weather involve far too many particles to analyze precisely with computers, but much of the essential behavior which makes these systems chaotic can also be found in much simpler systems that are much more easily analyzed with pencil and paper and simulated with computers. This sensitive dependence on initial conditions also guarantees that weather forecasting will not be accurate for more than a few days in advance.Ĭhaos can also be seen in systems as diverse as electrical circuits, oscillating chemical reactions, and fluid dynamics, and planetary bodies orbiting each other. The "butterfly effect" is an example of this, alluding to the idea that the flap of a butterfly's wings in Africa can cause a cascade of events culminating in a tornado in Texas. This means that if two copies of the system differ by only a very small amount, then after a relatively short period of time, the two systems will diverge and appear very different from each other. Individual molecules of air all conform to basic laws of physics, but global weather patterns are anything but simple.Ī hallmark of chaotic systems is sensitive dependence on initial conditions. A classic example of this is the weather. I don't know if you consider that "using an object".Chaos theory is the study of how systems that follow simple, straightforward, deterministic laws can exhibit very complicated and seemingly random long term behavior. Return for y in range(size)]Īctually, tick() would be even better written using a collections.Counter. Or xy in live_cells and neighbor_count = 2) Neighbor_count = 1 + neighbor_count.get(neighbor, 0) """ Takes a set of coordinates of live cells, and returns a set ofĬoordinates of the live cells in the next generation. I'd rewrite three functions as follows (and eliminate neighbors_count(), next_state(), and add_to_grid_alive(): def tick(live_cells): Construct the next state from scratch rather than by mutation: test_array_dict = tick(test_array_dict).Rename print_grid() to grid(), since it actually doesn't print anything.
Represent the board as a set of live cells, rather than a dict.Take advantage of list/set/dict comprehensions more.In addition to the change in algorithm, I also recommend: You count each cell's neighbors! But the number of neighbors is precisely the amount of overlapped processing that would have occurred had you not bothered to deduplicate the to_check list to begin with! So, instead of drawing a list of interesting cells and counting their neighbors, why not just have each existing cell increment the neighbor count of each neighboring coordinate? Then, once you have that list to_check, what do you do with it? for item in to_check: In other words, make a list of the neighbors of each cell, but make sure that each coordinate is listed just once.
The algorithm that you use, though, is cumbersome, particularly illustrated by these few lines: for item in cells.keys():Ĭhecking = ,item) if x not in to_check and x not in cells ] That is a good representation for sparse boards, but not so much for crowded boards. You're representing the cells mainly using a dictionary of coordinates, converting to a two-dimensional array only for the purposes of printing the output.
CONWAYS GAME OF LIFE HEAT MAP CODE
I added = 0 ] to the tick function and it really sped up the the code on higher iterations Neighbors = neighbors_count(point,point,cells)Įlif neighbors > 3 or neighbors >', x + 1įor item in print_grid(20,test_array_dict): I'm wondering if there is a better way to check the surrounding points or if storing the active points in a dictionary is a bad idea. It returns a dictionary of living points on a grid and points that were alive at some point. I tried to solve it without using objects. I was wondering if anyone could provide some feedback on my solution to Conway's game of life.
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