To avoid redundancy, however, we only show the implementation for the sparse representation in this article. Figure 7 shows the implementation of the sparse representation. It is made up of a single attribute, the grid , which records the positions of living cells in a set.
Figure 8 shows the rules of the game. Figure 9 shows an example on how to run the game with the configurations of Figure 5. In Figure 11, we show the type definitions for our Haskell implementation. We only implemented the sparse variant.
We make use of newtype wrappers to encapsulate our main types. The Board, or grid, is simply a list of the coordinates of live cells. TallyState is a State Monad containing the Map in which we tally the living neighbours of cells. Finally, the Rules and Neighbours types represent the functions that return the fate of a cell, and a list of its neighbours, respectively.
In Figure 12, we show a set of functions for our game. The advance function applies the rules to current state and returns a new state. Finally, in Figure 13, we implement our main function and the standard rules. As mentioned earlier, we want to compare the speed and elegance of the different representations. For a board size of 80x80, iterations and initial configuration of 39,40 , 39,41 , 40,39 , 40,40 , 41, The result is shown in Figure The respective computation times are:. Haskell, sparse: 0. For our second test, we used a x board, and ran a iteration simulation, starting from the following initial configuration:.
This resulted in what we see in Figure 15, the respective computation times are:.roytradrolfaigent.ml
From Scratch: The Game of Life
From these two tests, it is clear that the dense representation in Python is much slower than the sparse representations in Haskell and Python. Between the two sparse representations provided, the Haskell one shows a marked improvement in computation time. Evaluating elegance of an implementation is a rather subjective task. We propose instead to show a few metrics for both implementations: effective lines of code, number of functions, and number of explicit conditional statements.
The Meaning of Life | The New Yorker
Code elegance, as such, relies heavily on personal favourites, we therefore leave the decision in the apt hands of the reader ;. Effective Lines of Code:. Number of functions:.
Dense Python representation: 6. On 19 June a surprising milestone was reached. It's since been reduced further, to 29 gliders, and eventually down to only 9 gliders as part of the long-running "in" project. This made it possible to announce a surprising result: there's a strict upper bound for the cost in gliders for any strict still life , assuming it can be constructed by colliding gliders at all. If a glider-constructible still life contains N ON cells, then it can be constructed with less than 2N gliders.
A Mix of Theory and Practice. For still lifes larger than 17 bits, this result is supplied by the strange and wonderful RCT method. The RCT reverse caber tosser is a pattern that is constructible with only 35 gliders, that reads the very faraway position of an approaching object to produce a stream of bits, which are then interpreted as a construction recipe fed to a universal construction arm. Cleanup of the RCT's mechanism would also have to be done to produce a full synthesis, which makes it tricky to create these glider recipes in practice; no working examples have yet been completed.
Read the whole story at b3s23life. For the last several years Adam P. Goucher has been incrementally working out the construction details for a "0E0P metacell". A metacell is a piece of Life circuitry that simulates the behavior of a single cell in Life, or in many cases some other CA rule, depending on how it's programmed.
This means that when the metacell needs to turn back on again, it must be re-constructed from the ground up by its neighbors. One of the important effects of this design is that metacell patterns run at a sufficiently high step size, when viewed from very far away e.
- Life - The Game;
- Akasha - The Game of Life.
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A key breakthrough enabling the construction of the 0E0P metacell was a publicly available search program written by Goucher, capable of finding a single-channel construction recipe for any constellation of still lifes -- provided the still lifes aren't too close together, and that recipes are known for each of them in isolation. This search program was originally called "slmake" but is now renamed to "slsparse" due to its ability to analyze a large constellation and automatically separate it into several well-separated sub-constellations, or "metaclusters" when that's possible.
The previous post summarized the new glider reverse caber tosser universal constructor design, but didn't go into detail about what exactly makes the design universal. Here are most of the fiddly details, some of which are already out of date now that a universal construction method has been found with as few as 35 gliders. See this conwaylife. These various switch engines are almost the only things that need to be constructed. Marriage and children usually occur during the game.
Players in could end up in the Poor Farm or land happily in Millionaire Acres.
Life - The Game
The version offers everyone more comfortable destinations, sending players to either Countryside Acres or Millionaire Estates. In any event, chance and luck play the largest part in the journey.
The game has been criticized over the years for being based solely on luck and for rewarding risk-taking, but Life has stood the test of time—and family game night would not be as much fun without it.