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Neighborhood logic established. Optimization needed

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Joshua Potter 2015-06-05 23:19:57 -04:00
parent 3917627234
commit cacbfe29ca
4 changed files with 104 additions and 74 deletions
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42
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
The following uses numpy/matplotlib underneath, and will ideally incorporate the following:
* Arbitrary description of neighborhoods
* Arbitrary leveling of bit planes
* Arbitrary description of rulesets
* 2D and 3D cellular automata
* Timing specifications for granular viewing
* Echoing and Tracing (for 2D)
* N-Dimensional Cellular Automata
* Arbitrary count of bit planes and description of neighborhoods
* Timing specifications and control for granular viewing
* ECHOing and TRACing in library for 2D CAMs
Documentation will be made available at fuzzykayak.com/... but a quickstart will be provided below.
There are also a variety of examples given to demonstrate different means of building CAMS.
Quickstart
----------
To begin construction of a CAM, we need two objects: a CAM and a Ruleset.
A CAM can be broken down into a list of cell planes, each of which contain the same number of states.
Of these planes, the first is considered the master, and all others are mirrors of the master at an
earlier stage in time (this allows for methods such as ECHOing).
A ruleset can further be broken down into a list of configurations, of which one must pass
for the state of a cell to change. During application of a ruleset, each cell is described by
a neighborhood, which packages all other cells considered in the given plane.
The following will construct Conway's Game of Life, as shown in the provided GIF:
```
import cam
import ruleset as rs
# View the different formats the CAMParser can parse. Manual construction for
# more complicated rulesets are also a possibility
c = cam.CAM(1, 100, 2)
p = u.CAMParser('B3/S23', c)
# 400 represents the time, in milliseconds, before the next tick occurs
c.randomize()
c.start_plot(400, p.ruleset)
```
![alt tag](https://raw.githubusercontent.com/jrpotter/fifth/master/rsrc/demo.gif)

13
src/cam.py
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@ -1,11 +1,10 @@
"""
Top level module representing a Cellular Automata Machine.
The CAM consists of any number of cell planes that allow for increasingly complex cellular automata.
The CAM consists of a number of cell planes that allow for increasingly complex cellular automata.
This is the top-level module that should be used by anyone wanting to work with fifth, and provides
all methods needed (i.e. supported) to interact/configure the cellular automata as desired.
all methods needed (i.e. supported) to interact/configure with the cellular automata directly.
@author: jrpotter
@date: June 01, 2015
"""
import time
@ -22,9 +21,9 @@ class CAM:
directly, but instead mirror the master plane, and reflect these changes after a given number of
"ticks."
A tick represents an interval of time after which all states should be updated, and, therefore, all
cell planes should be updated. Certain planes may or may not change every tick, but instead on every
nth tick, allowing for more sophisticated views such as ECHOing and TRACE-ing.
A tick represents an interval of time after which all states of a given set of cell planes should be
updated. should be updated, Certain planes may or may not change every tick, but instead on every
nth tick, allowing for more sophisticated views such as ECHOing and TRACing.
"""
def __init__(self, cps=1, states=100, dimen=2):
@ -49,7 +48,7 @@ class CAM:
The tick function should be called whenever we want to change the current status of the grid.
Every time the tick is called, the ruleset is applied to each cell and the next set of states
is placed into the master grid. Depending on the timing specifications set by the user, this
may also change secondary cell planes (the master is always updated on each tick).
may also change secondary cell planes (the master, by default, is always updated on each tick).
"""
self.total += 1
for i, j in self.ticks:

2
src/neighborhood.py
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@ -8,7 +8,7 @@ class Neighborhood:
"""
"""
def __init__(self, index, offsets):
def __init__(self, f_index, b_offset, states, indices):
"""
"""

119
src/ruleset.py
View File

@ -4,11 +4,9 @@ The following determines the next state of a given cell in a CAM.
The ruleset takes in a collection of rules specifying neighborhoods, as well as the configurations of
said neighborhood that yield an "on" or "off" state on the cell a ruleset is being applied to.
@author: jrpotter
@date: May 31st, 2015
"""
import enum
import itertools as it
import numpy as np
@ -27,19 +25,20 @@ class Ruleset:
must match exactly for the center cell to be a 1, then each cell is checked for this configuration, and its
state is updated afterward (note the above is merely for clarity; a configuration is not defined as such). Note
configurations are checked until a match occurs, in a FIFO manner.
configurations are checked until a match occurs, in order of the configurations list.
"""
class Method(enum.Enum):
"""
Specifies how a ruleset should be applied to a given cell.
* A match declares that a given configuration must match exactly for the cell to be considered on.
* A tolerance specifies that a configuration must match within a given percentage to be considered on.
* A match declares that a given configuration must match exactly for a configuration to pass
* A tolerance specifies that a configuration must match within a given percentage to pass
* A specification allows the user to define a custom function which must return a boolean, declaring
whether a cell should be on or off. This function is given the current cell's state, as well as
the state of the cell's neighbors.
whether a configuration passes. This function is given a neighborhood with all necessary information.
* Always passing allows the first configuration to always yield a success. It is redundant to add
any additional configurations in this case (in fact it is inefficient since neighborhoods are computer
in advance).
"""
MATCH = 0
TOLERATE = 1
@ -48,66 +47,24 @@ class Ruleset:
def __init__(self, method):
"""
@grid: Every ruleset is bound to a grid, which a ruleset is applied to.
@method: One of the values defined in the RulesetMethod enumeration. View class for description.
A ruleset does not begin with any configurations; only a means of verifying them.
@method: One of the values defined in the Ruleset.Method enumeration. View class for description.
"""
self.method = method
self.configurations = []
def addConfiguration(self, grid, next_state, offsets):
"""
Creates a configuration and saves said configuration.
"""
config = Configuration(grid, next_state, offsets)
self.configurations.append(config)
def applyTo(self, plane, *args):
"""
Depending on the set method, applies ruleset to each cell in the plane.
Note we first compute all neighborhoods in a batch manner and then test that a configuration
passes on the supplied neighborhood.
@args: If our method is TOLERATE, we pass in a value in set [0, 1]. This specifies the threshold between a
passing (i.e. percentage of matches in a configuration is > arg) and failing. If our method is SATISFY,
arg should be a function returning a BOOL, which takes in a current cell's value, and the
value of its neighbors.
"""
master = plane.grid.flat
for config in self.configurations:
# Construct neighborhoods
#
# After profiling with a previous version, I found that going through each index and totaling the number
# of active states was taking much longer than I liked. Instead, we compute as many neighborhoods as possible
# simultaneously, avoiding explicit summation via the "sum" function, at least for each state separately.
#
# Because the states are now represented as numbers, we instead convert each number to their binary representation
# and add the binary representations together. We do this in chunks of 9, depending on the number of offsets, so
# no overflowing of a single column can occur. We can then find the total of the ith neighborhood by checking the
# sum of the ith index of the summation of every 9 chunks of numbers (this is done a row at a time).
# TODO: Config offsets should be flat index, bit offset
neighborhoods = []
values = []
for f_index, offset in config.offsets:
val = plane.f_bits([f_index])
values.append(int(val[offset+1:] + val[:offset]))
# Chunk into groups of 9 and sum all values
chunks = [values[i:i+9] for i in range(0, len(values), 9)]
summands = map(sum, chunks)
# Construct neighborhoods for each value in list
# Determine which function should be used to test success
if self.method == Ruleset.Method.MATCH:
vfunc = self._matches
elif self.method == Ruleset.Method.TOLERATE:
@ -117,13 +74,57 @@ class Ruleset:
elif self.method == Ruleset.Method.ALWAYS_PASS:
vfunc = lambda *args: True
# Apply the function if possible
passed, state = config.passes(f_index, grid, vfunc, *args)
# Find the set of neighborhoods for each given configuration
neighborhoods = [self._construct_neighborhoods(plane, config) for c in self.configurations]
for f_idx, value in enumerate(self.plane.flat):
for b_offset in len(self.plane.shape[-1]):
for c_idx, config in enumerate(self.configurations):
n_idx = f_idx * self.plane.shape[-1] + b_offset
passed, state = config.passes(neighborhoods[c_idx][n_idx], vfunc, *args)
if passed:
return state
plane[f_idx][b_offset] = state
break
# If no configuration passes, we leave the state unchanged
return grid.flat[f_index]
def _construct_neighborhoods(self, plane, config):
"""
Construct neighborhoods
After profiling with a previous version, I found that going through each index and totaling the number
of active states was taking much longer than I liked. Instead, we compute as many neighborhoods as possible
simultaneously, avoiding explicit summation via the "sum" function, at least for each state separately.
Because the states are now represented as numbers, we instead convert each number to their binary representation
and add the binary representations together. We do this in chunks of 9, depending on the number of offsets, so
no overflowing of a single column can occur. We can then find the total of the ith neighborhood by checking the
sum of the ith index of the summation of every 9 chunks of numbers (this is done a row at a time).
TODO: Config offsets should be flat offset, bit offset
"""
neighborhoods = []
for f_idx, row in enumerate(plane.grid.flat):
# Construct the current neighborhoods of each bit beforehand
row_neighborhoods = [Neighborhood(f_idx, i) for i in range(plane.shape[-1])]
# Note: config's offsets contain the index of the number in the plane's flat iterator
# and the offset of the bit referring to the actual state in the given neighborhood
offset_totals = []
for f_offset, b_offset in config.offsets:
row_offset = plane.f_bits(f_idx + f_offset)
offset_totals.append(int(row_offset[b_offset+1:] + row_offset[:b_offset]))
# Chunk into groups of 9 and sum all values
# These summations represent the total number of states in a given neighborhood
chunks = map(sum, [offset_totals[i:i+9] for i in range(0, len(offset_totals), 9)])
for chunk in chunks:
for i in range(len(row_neighborhoods)):
row_neighborhoods[i].total += int(chunk[i])
# Lastly, keep neighborhoods 1D, to easily relate to the flat plane grid
neighborhoods += row_neighborhoods
return neighborhoods
def _matches(self, f_index, f_grid, indices, states):
"""