1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
|
<html>
<title>Golly Help: RuleLoader</title>
<body bgcolor="#FFFFCE">
<p>
The RuleLoader algorithm allows rules to be specified in external files.
Given the rule string "Foo", RuleLoader will search for a file called Foo.rule.
The format of a .rule file is described <a href="../formats.html#rule">here</a>.
A number of examples can be found in the Rules folder:
<p><b><a href="rule:B3/S23">B3/S23</a></b> or <b><a href="rule:Life">Life</a></b><br>
Conway's Life. This is the default rule for the RuleLoader algorithm and is built in
(there is no corresponding .rule file).
<p><b><a href="rule:Banks-I">Banks-I</a>,
<a href="rule:Banks-II">Banks-II</a>,
<a href="rule:Banks-III">Banks-III</a>,
<a href="rule:Banks-IV">Banks-IV</a></b><br>
In 1971, Edwin Roger Banks (a student of Ed Fredkin) made simpler versions of Codd's 1968 CA,
using only two states in some cases. These four rules are found in his PhD thesis.
To see the rules in action, open
<a href="open:Patterns/Banks/Banks-I-demo.rle">Banks-I-demo.rle</a>
and the other examples in Patterns/Banks/.
<p><b><a href="rule:BBM-Margolus-emulated">BBM-Margolus-emulated</a></b><br>
Ed Fredkin's Billiard Ball Model, using the Margolus neighborhood to implement a simple reversible
physics of bouncing balls.
In this implementation we are emulating the system using a Moore-neighborhood CA with extra states.
Open <a href="open:Patterns/Margolus/BBM.rle">BBM.rle</a> to see the rule in action.
<p><b><a href="rule:BriansBrain">BriansBrain</a></b><br>
An alternative implementation of the Generations rule /2/3.
<p><b><a href="rule:Byl-Loop">Byl-Loop</a></b><br>
A six state 5-neighborhood CA that supports small self-replicating loops.
To see the rule in action, open
<a href="open:Patterns/Loops/Byl-Loop.rle">Byl-Loop.rle</a>.
<p><b><a href="rule:Caterpillars">Caterpillars</a></b><br>
An alternative implementation of the Generations rule 124567/378/4.
<p><b><a href="rule:Chou-Reggia-1">Chou-Reggia-1</a></b> and
<b><a href="rule:Chou-Reggia-2">Chou-Reggia-2</a></b><br>
Two 5-neighborhood CA that supports tiny self-replicating loops.
To see the rules in action, open
<a href="open:Patterns/Loops/Chou-Reggia-Loop-1.rle">Chou-Reggia-Loop-1.rle</a> and
<a href="open:Patterns/Loops/Chou-Reggia-Loop-2.rle">Chou-Reggia-Loop-2.rle</a>.
<p><b><a href="rule:Codd">Codd</a></b><br>
In 1968, Edgar F. Codd (who would later invent the relational database) made a simpler version
of von Neumann's 29-state CA, using just 8 states. To see the rule in action, open
<a href="open:Patterns/Codd/repeater-emitter-demo.rle">repeater-emitter-demo.rle</a>
and the other examples in Patterns/Codd/.
<p><b><a href="rule:Codd2">Codd2</a></b><br>
A very minor extension of Codd's transition table, to allow for some sheathing cases that
were found with large patterns.
See <a href="open:Patterns/Codd/sheathing-problems.rle">sheathing-problems.rle</a>
for a demonstration of the problem cases.
<p><b><a href="rule:CrittersMargolus_emulated">CrittersMargolus_emulated</a></b><br>
The Critters rule is reversible and has Life-like gliders.
See <a href="open:Patterns/Margolus/CrittersCircle.rle">CrittersCircle.rle</a>.
<p><b><a href="rule:Devore">Devore</a></b><br>
In 1973, John Devore altered Codd's transition table to allow for simple diodes and triodes,
enabling him to make a much smaller replicator than Codd's.
See <a href="open:Patterns/Devore/Devore-rep.rle">Devore-rep.rle</a>
and the other examples in Patterns/Devore/.
<p><b><a href="rule:DLA-Margolus-emulated">DLA-Margolus-emulated</a></b><br>
<a href="http://en.wikipedia.org/wiki/Diffusion-limited_aggregation">Diffusion-limited aggregation</a>
(DLA) is where moving particles can become stuck, forming a distinctive fractal pattern seen in several
different natural physical systems. See <a href="open:Patterns/Margolus/DLA.rle">DLA.rle</a>.
<p><b><a href="rule:Ed-rep">Ed-rep</a></b><br>
A version of Fredkin's parity rule, for 7 states.
See <a href="open:Patterns/Other-Rules/Ed-rep.rle">Ed-rep.rle</a> for an image of Ed Fredkin
that photocopies itself.
<p><b><a href="rule:Evoloop">Evoloop</a></b> and
<b><a href="rule:Evoloop-finite">Evoloop-finite</a></b><br>
An extension of the SDSR Loop, designed to allow evolution through collisions.
To see the rule in action, open
<a href="open:Patterns/Loops/Evoloop-finite.rle">Evoloop-finite.rle</a>.
<p><b><a href="rule:HPP">HPP</a></b><br>
The HPP lattice gas. A simple model of gas particles moving at right angles at a fixed speed turns out to give an
accurate model of fluid dynamics on a larger scale. Though the later FHP gas improved on the HPP gas by using a
hexagonal lattice for more realistic results, the HPP gas is where things began.
Open <a href="open:Patterns/Other-Rules/HPP-demo.rle">HPP-demo.rle</a>.
<p><b><a href="rule:Langtons-Ant">Langtons-Ant</a></b><br>
Chris Langton's other famous CA. An ant walks around on a binary landscape, collecting and depositing pheremones.
See <a href="open:Patterns/Other-Rules/Langtons-Ant.rle">Langtons-Ant.rle</a>.
<p><b><a href="rule:Langtons-Loops">Langtons-Loops</a></b><br>
The original loop. Chris Langton adapted Codd's 1968 CA to support a simple form of
self-replication based on a circulating loop of instructions.
To see the rule in action, open
<a href="open:Patterns/Loops/Langtons-Loops.rle">Langtons-Loops.rle</a>.
<p><b><a href="rule:LifeHistory">LifeHistory</a></b><br>
A 7-state extension of the HistoricalLife rule from MCell, allowing for on and off marked cells (states 3 and 4) as
well as the history envelope (state 2). State 3 is useful for labels and other identifying marks, since an active
pattern can touch or even cross it without being affected. State 5 is an alternate marked ON state most often
used to mark a 'starting' location; once a cell changes to state 2, it can not return to this start state.
State 6 cells kill any adjacent live cells; they are intended to be used as boundaries between subpatterns, e.g.
in an active stamp collection where flying debris from one subpattern might adversely affect another subpattern.
See <a href="open:Patterns/Life/Signal-Circuitry/Herschel-conduit-stamp-collection.rle">Herschel-conduit-stamp-collection.rle</a>
for an example using all of LifeHistory's extra states.
<p><b><a href="rule:LifeOnTheEdge">LifeOnTheEdge</a></b><br>
A CA proposed by Franklin T. Adams-Watters in which all the action occurs on
the edges of a square grid. Each edge can be on or off and has six neighbors,
three at each end. An edge is on in the next generation iff exactly two of the
edges in its seven edge neighborhood (including the edge itself) are on.
This implementation has 3 live states with suitable icons that allow any pattern
of edges to be created.
Open <a href="open:Patterns/Other-Rules/life-on-the-edge.rle">life-on-the-edge.rle</a>.
<p><b><a href="rule:LifeOnTheSlope">LifeOnTheSlope</a></b><br>
The same behavior as LifeOnTheEdge but patterns are rotated by 45 degrees.
This implementation has only 2 live states (with icons \ and /), so it's a lot easier
to enter patterns and they run faster.
Open <a href="open:Patterns/Other-Rules/life-on-the-slope.rle">life-on-the-slope.rle</a>.
<p><b><a href="rule:Perrier">Perrier</a></b><br>
Perrier extended Langton's Loops to allow for universal computation.
See <a href="open:Patterns/Loops/Perrier-Loop.rle">Perrier-Loop.rle</a>.
<p><b><a href="rule:Sand-Margolus-emulated">Sand-Margolus-emulated</a></b><br>
MCell's Sand rule is a simple simulation of falling sand particles.
See <a href="open:Patterns/Margolus/Sand.rle">Sand.rle</a>.
<p><b><a href="rule:SDSR-Loop">SDSR-Loop</a></b><br>
An extension of Langton's Loops, designed to cause dead loops to disappear,
allowing other loops to replicate further.
To see the rule in action, open
<a href="open:Patterns/Loops/SDSR-Loop.rle">SDSR-Loop.rle</a>.
<p><b><a href="rule:StarWars">StarWars</a></b><br>
An alternative implementation of the Generations rule 345/2/4.
<p><b><a href="rule:Tempesti">Tempesti</a></b><br>
A programmable loop that can construct shapes inside itself after replication.
To see the rule in action, open
<a href="open:Patterns/Loops/Tempesti-Loop.rle">Tempesti-Loop.rle</a>.
This loop prints the letters 'LSL' inside each copy — the initials of Tempesti's university group.
<p><b><a href="rule:TMGasMargolus_emulated">TMGasMargolus_emulated</a></b><br>
A different version of the HPP gas, implemented in the Margolus neighborhood, see
<a href="open:Patterns/Margolus/TMGas.rle">TMGas.rle</a>.
<p><b><a href="rule:TripATronMargolus_emulated">TripATronMargolus_emulated</a></b><br>
The Trip-A-Tron rule in the Margolus neighborhood.
See <a href="open:Patterns/Margolus/TripATron.rle">TripATron.rle</a>.
<p><b><a href="rule:WireWorld">WireWorld</a></b><br>
A 4-state CA created by Brian Silverman.
WireWorld models the flow of currents in wires and makes it relatively
easy to build logic gates and other digital circuits.
Open <a href="open:Patterns/WireWorld/primes.mc">primes.mc</a>
and the other examples in Patterns/WireWorld/.
<p><b><a href="rule:Worm-1040512">Worm-1040512</a>,
<a href="rule:Worm-1042015">Worm-1042015</a>,
<a href="rule:Worm-1042020">Worm-1042020</a>,
<a href="rule:Worm-1252121">Worm-1252121</a>,
<a href="rule:Worm-1525115">Worm-1525115</a></b><br>
Examples of Paterson's Worms, a simulation created by Mike Paterson in which a
worm travels around a triangular grid according to certain rules.
There's also a rule called <b><a href="rule:Worm-complement">Worm-complement</a></b>
which can be used to show the uneaten edges within a solid region.
Open <a href="open:Patterns/Patersons-Worms/worm-1040512.rle">worm-1040512.rle</a>
and the other examples in Patterns/Patersons-Worms/.
<p>
<font size=+1><b>References:</b></font>
<p><b>Banks-I, Banks-II, Banks-III, Banks-IV</b> (1971)<br>
<i>E. R. Banks. "Information Processing and Transmission in Cellular Automata" PhD Thesis, MIT, 1971.</i>
<p><b>Byl-Loop</b> (1989)<br>
<i>J. Byl. "Self-Reproduction in small cellular automata." Physica D, Vol. 34, pages 295-299, 1989.</i>
<p><b>Chou-Reggia-1</b> and <b>Chou-Reggia-2</b> (1993)<br>
<i>J. A. Reggia, S. L. Armentrout, H.-H. Chou, and Y. Peng.
"Simple systems that exhibit self-directed replication."
Science, Vol. 259, pages 1282-1287, February 1993.</i>
<p><b>Codd</b> (1968)<br>
<i>E. F. Codd, "Cellular Automata" Academic Press, New York, 1968.</i>
<p><b>Devore</b> (1973)<br>
<i>Devore, J. and Hightower, R. (1992) "The Devore variation of the Codd self-replicating computer"
Third Workshop on Artificial Life, Santa Fe, New Mexico,
Original work carried out in the 1970s though apparently never published.
Reported by John R. Koza, "Artificial life: spontaneous emergence of
self-replicating and evolutionary self-improving computer programs,"
in Christopher G. Langton, Artificial Life III, Proc. Volume XVII
Santa Fe Institute Studies in the Sciences of Complexity,
Addison-Wesley Publishing Company, New York, 1994, p. 260.</i>
<p><b>Evoloop</b> (1999)<br>
<i>Hiroki Sayama "Toward the Realization of an Evolving Ecosystem on Cellular Automata",
Proceedings of the Fourth International Symposium on Artificial Life and Robotics (AROB 4th '99),
M. Sugisaka and H. Tanaka, eds., pp.254-257, Beppu, Oita, Japan, 1999.</i>
<p><b>HPP</b> (1973)<br>
<i>J. Hardy, O. de Pazzis, and Y. Pomeau. J. Math. Phys. 14, 470, 1973.</i>
<p><b>Langtons-Ant</b> (1986)<br>
<i>C. G. Langton. "Studying artificial life with cellular automata" Physica D 2(1-3):120-149, 1986.</i>
<p><b>Langtons-Loops</b> (1984)<br>
<i>C. G. Langton. "Self-reproduction in cellular automata." Physica D, Vol. 10, pages 135-144, 1984.</i>
<p><b>Paterson's Worms</b> (1973)<br>
See these sites for a good description and the latest results:</a><br>
<a href="http://www.maa.org/editorial/mathgames/mathgames_10_24_03.html">http://www.maa.org/editorial/mathgames/mathgames_10_24_03.html</a><br>
<a href="http://wso.williams.edu/%7Ebchaffin/patersons_worms/">http://wso.williams.edu/~Ebchaffin/patersons_worms/</a><br>
<a href="http://tomas.rokicki.com/worms.html">http://tomas.rokicki.com/worms.html</a>
<p><b>Perrier</b> (1996)<br>
<i>J.-Y. Perrier, M. Sipper, and J. Zahnd.
<a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.3200">"Toward a viable, self-reproducing universal computer"</a>
Physica D 97: 335-352. 1996</i>
<p><b>SDSR-Loop</b> (1998)<br>
<i>Hiroki Sayama. "Introduction of Structural Dissolution into Langton's Self-Reproducing Loop."
Artificial Life VI: Proceedings of the Sixth International Conference on Artificial Life,
C. Adami, R. K. Belew, H. Kitano, and C. E. Taylor, eds., pp.114-122, Los Angeles, California, 1998, MIT Press.</i>
<p><b>Tempesti</b> (1995)<br>
<i>G. Tempesti. "A New Self-Reproducing Cellular Automaton Capable of Construction and Computation".
Advances in Artificial Life, Proc. 3rd European Conference on Artificial Life, Granada, Spain, June 4-6, 1995,
Lecture Notes in Artificial Intelligence, 929, Springer Verlag, Berlin, 1995, pp. 555-563.</i>
<p><b>WireWorld</b> (1987)<br>
<i>A. K. Dewdney, Computer Recreations. Scientific American 282:136-139, 1990.</i>
</body>
</html>
|