Neighborhood logic established. Optimization needed
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README.md
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README.md
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@ -7,11 +7,41 @@ though mentioned as reasonably priced, a CAM Forth machine is out of my price ra
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The following uses numpy/matplotlib underneath, and will ideally incorporate the following:
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* Arbitrary description of neighborhoods
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* Arbitrary leveling of bit planes
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* Arbitrary description of rulesets
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* 2D and 3D cellular automata
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* Timing specifications for granular viewing
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* Echoing and Tracing (for 2D)
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* N-Dimensional Cellular Automata
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* Arbitrary count of bit planes and description of neighborhoods
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* Timing specifications and control for granular viewing
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* ECHOing and TRACing in library for 2D CAMs
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Documentation will be made available at fuzzykayak.com/... but a quickstart will be provided below.
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There are also a variety of examples given to demonstrate different means of building CAMS.
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Quickstart
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----------
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To begin construction of a CAM, we need two objects: a CAM and a Ruleset.
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A CAM can be broken down into a list of cell planes, each of which contain the same number of states.
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Of these planes, the first is considered the master, and all others are mirrors of the master at an
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earlier stage in time (this allows for methods such as ECHOing).
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A ruleset can further be broken down into a list of configurations, of which one must pass
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for the state of a cell to change. During application of a ruleset, each cell is described by
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a neighborhood, which packages all other cells considered in the given plane.
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The following will construct Conway's Game of Life, as shown in the provided GIF:
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```
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import cam
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import ruleset as rs
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# View the different formats the CAMParser can parse. Manual construction for
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# more complicated rulesets are also a possibility
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c = cam.CAM(1, 100, 2)
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p = u.CAMParser('B3/S23', c)
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# 400 represents the time, in milliseconds, before the next tick occurs
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c.randomize()
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c.start_plot(400, p.ruleset)
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```
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![alt tag](https://raw.githubusercontent.com/jrpotter/fifth/master/rsrc/demo.gif)
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13
src/cam.py
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src/cam.py
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@ -1,11 +1,10 @@
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"""
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Top level module representing a Cellular Automata Machine.
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The CAM consists of any number of cell planes that allow for increasingly complex cellular automata.
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The CAM consists of a number of cell planes that allow for increasingly complex cellular automata.
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This is the top-level module that should be used by anyone wanting to work with fifth, and provides
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all methods needed (i.e. supported) to interact/configure the cellular automata as desired.
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all methods needed (i.e. supported) to interact/configure with the cellular automata directly.
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@author: jrpotter
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@date: June 01, 2015
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"""
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import time
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@ -22,9 +21,9 @@ class CAM:
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directly, but instead mirror the master plane, and reflect these changes after a given number of
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"ticks."
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A tick represents an interval of time after which all states should be updated, and, therefore, all
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cell planes should be updated. Certain planes may or may not change every tick, but instead on every
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nth tick, allowing for more sophisticated views such as ECHOing and TRACE-ing.
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A tick represents an interval of time after which all states of a given set of cell planes should be
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updated. should be updated, Certain planes may or may not change every tick, but instead on every
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nth tick, allowing for more sophisticated views such as ECHOing and TRACing.
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"""
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def __init__(self, cps=1, states=100, dimen=2):
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@ -49,7 +48,7 @@ class CAM:
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The tick function should be called whenever we want to change the current status of the grid.
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Every time the tick is called, the ruleset is applied to each cell and the next set of states
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is placed into the master grid. Depending on the timing specifications set by the user, this
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may also change secondary cell planes (the master is always updated on each tick).
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may also change secondary cell planes (the master, by default, is always updated on each tick).
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"""
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self.total += 1
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for i, j in self.ticks:
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@ -8,7 +8,7 @@ class Neighborhood:
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"""
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"""
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def __init__(self, index, offsets):
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def __init__(self, f_index, b_offset, states, indices):
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"""
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"""
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src/ruleset.py
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src/ruleset.py
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@ -4,11 +4,9 @@ The following determines the next state of a given cell in a CAM.
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The ruleset takes in a collection of rules specifying neighborhoods, as well as the configurations of
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said neighborhood that yield an "on" or "off" state on the cell a ruleset is being applied to.
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@author: jrpotter
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@date: May 31st, 2015
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"""
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import enum
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import itertools as it
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import numpy as np
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@ -27,19 +25,20 @@ class Ruleset:
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must match exactly for the center cell to be a 1, then each cell is checked for this configuration, and its
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state is updated afterward (note the above is merely for clarity; a configuration is not defined as such). Note
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configurations are checked until a match occurs, in a FIFO manner.
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configurations are checked until a match occurs, in order of the configurations list.
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"""
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class Method(enum.Enum):
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"""
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Specifies how a ruleset should be applied to a given cell.
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* A match declares that a given configuration must match exactly for the cell to be considered on.
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* A tolerance specifies that a configuration must match within a given percentage to be considered on.
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* A match declares that a given configuration must match exactly for a configuration to pass
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* A tolerance specifies that a configuration must match within a given percentage to pass
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* A specification allows the user to define a custom function which must return a boolean, declaring
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whether a cell should be on or off. This function is given the current cell's state, as well as
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the state of the cell's neighbors.
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whether a configuration passes. This function is given a neighborhood with all necessary information.
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* Always passing allows the first configuration to always yield a success. It is redundant to add
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any additional configurations in this case (in fact it is inefficient since neighborhoods are computer
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in advance).
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"""
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MATCH = 0
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TOLERATE = 1
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@ -48,82 +47,84 @@ class Ruleset:
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def __init__(self, method):
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"""
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@grid: Every ruleset is bound to a grid, which a ruleset is applied to.
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@method: One of the values defined in the RulesetMethod enumeration. View class for description.
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A ruleset does not begin with any configurations; only a means of verifying them.
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@method: One of the values defined in the Ruleset.Method enumeration. View class for description.
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"""
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self.method = method
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self.configurations = []
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def addConfiguration(self, grid, next_state, offsets):
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"""
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Creates a configuration and saves said configuration.
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"""
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config = Configuration(grid, next_state, offsets)
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self.configurations.append(config)
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def applyTo(self, plane, *args):
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"""
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Depending on the set method, applies ruleset to each cell in the plane.
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Note we first compute all neighborhoods in a batch manner and then test that a configuration
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passes on the supplied neighborhood.
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@args: If our method is TOLERATE, we pass in a value in set [0, 1]. This specifies the threshold between a
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passing (i.e. percentage of matches in a configuration is > arg) and failing. If our method is SATISFY,
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arg should be a function returning a BOOL, which takes in a current cell's value, and the
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value of its neighbors.
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"""
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master = plane.grid.flat
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for config in self.configurations:
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# Determine which function should be used to test success
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if self.method == Ruleset.Method.MATCH:
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vfunc = self._matches
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elif self.method == Ruleset.Method.TOLERATE:
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vfunc = self._tolerates
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elif self.method == Ruleset.Method.SATISFY:
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vfunc = self._satisfies
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elif self.method == Ruleset.Method.ALWAYS_PASS:
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vfunc = lambda *args: True
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# Construct neighborhoods
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#
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# After profiling with a previous version, I found that going through each index and totaling the number
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# of active states was taking much longer than I liked. Instead, we compute as many neighborhoods as possible
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# simultaneously, avoiding explicit summation via the "sum" function, at least for each state separately.
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#
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# Because the states are now represented as numbers, we instead convert each number to their binary representation
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# and add the binary representations together. We do this in chunks of 9, depending on the number of offsets, so
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# no overflowing of a single column can occur. We can then find the total of the ith neighborhood by checking the
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# sum of the ith index of the summation of every 9 chunks of numbers (this is done a row at a time).
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# Find the set of neighborhoods for each given configuration
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neighborhoods = [self._construct_neighborhoods(plane, config) for c in self.configurations]
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for f_idx, value in enumerate(self.plane.flat):
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for b_offset in len(self.plane.shape[-1]):
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for c_idx, config in enumerate(self.configurations):
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n_idx = f_idx * self.plane.shape[-1] + b_offset
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passed, state = config.passes(neighborhoods[c_idx][n_idx], vfunc, *args)
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if passed:
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plane[f_idx][b_offset] = state
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break
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# TODO: Config offsets should be flat index, bit offset
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def _construct_neighborhoods(self, plane, config):
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"""
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Construct neighborhoods
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After profiling with a previous version, I found that going through each index and totaling the number
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of active states was taking much longer than I liked. Instead, we compute as many neighborhoods as possible
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simultaneously, avoiding explicit summation via the "sum" function, at least for each state separately.
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Because the states are now represented as numbers, we instead convert each number to their binary representation
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and add the binary representations together. We do this in chunks of 9, depending on the number of offsets, so
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no overflowing of a single column can occur. We can then find the total of the ith neighborhood by checking the
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sum of the ith index of the summation of every 9 chunks of numbers (this is done a row at a time).
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neighborhoods = []
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TODO: Config offsets should be flat offset, bit offset
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"""
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neighborhoods = []
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values = []
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for f_index, offset in config.offsets:
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val = plane.f_bits([f_index])
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values.append(int(val[offset+1:] + val[:offset]))
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for f_idx, row in enumerate(plane.grid.flat):
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# Construct the current neighborhoods of each bit beforehand
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row_neighborhoods = [Neighborhood(f_idx, i) for i in range(plane.shape[-1])]
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# Note: config's offsets contain the index of the number in the plane's flat iterator
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# and the offset of the bit referring to the actual state in the given neighborhood
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offset_totals = []
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for f_offset, b_offset in config.offsets:
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row_offset = plane.f_bits(f_idx + f_offset)
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offset_totals.append(int(row_offset[b_offset+1:] + row_offset[:b_offset]))
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# Chunk into groups of 9 and sum all values
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chunks = [values[i:i+9] for i in range(0, len(values), 9)]
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summands = map(sum, chunks)
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# These summations represent the total number of states in a given neighborhood
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chunks = map(sum, [offset_totals[i:i+9] for i in range(0, len(offset_totals), 9)])
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for chunk in chunks:
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for i in range(len(row_neighborhoods)):
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row_neighborhoods[i].total += int(chunk[i])
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# Construct neighborhoods for each value in list
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# Lastly, keep neighborhoods 1D, to easily relate to the flat plane grid
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neighborhoods += row_neighborhoods
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if self.method == Ruleset.Method.MATCH:
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vfunc = self._matches
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elif self.method == Ruleset.Method.TOLERATE:
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vfunc = self._tolerates
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elif self.method == Ruleset.Method.SATISFY:
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vfunc = self._satisfies
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elif self.method == Ruleset.Method.ALWAYS_PASS:
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vfunc = lambda *args: True
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# Apply the function if possible
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passed, state = config.passes(f_index, grid, vfunc, *args)
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if passed:
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return state
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# If no configuration passes, we leave the state unchanged
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return grid.flat[f_index]
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return neighborhoods
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def _matches(self, f_index, f_grid, indices, states):
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"""
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