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
|
var k = 5;
function repeatString(string, nTimes)
{
/*
Repeats a string n times
E.g. repeatString("hi", 10) -> "hihihihihihihihihihi"
*/
return Array(nTimes+1).join(string);
}
function pad(x, nDigits)
{
/* pad("33", 10) -> "0000000033" */
for (var s = x; s.length < nDigits; s = "0" + s);
return s;
}
function bin(x, nDigits)
{
/*
Returns an n-digit binary representation of x, adding zeros to the start if necessary.
E.g. bin(3, 11) -> "00000000011"
*/
for (var s = x.toString(2) /* Convert to binary */; s.length < nDigits; s = "0" + s /* Add zero to start */);
return s;
}
function check(b, msg)
{
/*
If b is false, it shows the error message to the user.
Returns b.
*/
if (!b)
{
$("#error").html(msg);
}
return b;
}
function startingConfigValid(sc)
{
/*
Returns true if sc is a valid starting configuration; if all of the characters in sc are 0 or 1.
*/
for (var i = 0; i < sc.length; i++)
{
if (sc[i] != '0' && sc[i] != '1')
return false;
}
return true;
}
function padConfiguration(config, size)
{
/* Place zeros before and after config so that config.length = size. */
for (; config.length < size-1; config = '0' + config + '0');
if (config.length < size)
config += '0'; /* Add zero at end if the number of zeros must be odd (e.g. padConfiguration("1101", 9) -> 001101000) */
return config;
}
function drawState(state, t)
{
/* Draws the states */
var w = $("#canvas").width();
var h = $("#canvas").height();
for (var i = 0; i < w; i++)
{
if (state[i] === '1')
ctx.fillRect(i*2, t*2, 2, 2);
}
}
function getNewValue(rule, above, c, binStrings)
{
/* Get new value of a cell given the cells above it. */
return rule[binStrings.indexOf(above)];
}
function startLoading()
{
$("#run").prop("disabled", true);
$("#run").html("Loading...");
}
function stopLoading()
{
$("#run").prop("disabled", false);
$("#run").html("Run");
}
function run()
{
$("#error").html("");
/* An elementary cellular automaton (e.g. Rule 110 (https://en.wikipedia.org/wiki/Rule_110)) */
var time = parseInt($("#time").val()); /* Amount of time to run the automaton for. */
var size = parseInt($("#size").val()); /* Size of the starting automaton (bits). */
var c = parseInt($("#c").val());
var startingConfig = $("#start").val(); /* Starting configuration for the automaton. */
var ruleNumber = parseInt($("#rule").val()); /* Rule number (e.g. 110). (0 <= x < 256) This must be converted to a binary number before use. */
if (!check(time > 0, "Error - The value " + time + " is an invalid time. Time > 0."))
{
/* Check for invalid time argument. */
stopLoading();
return;
}
if (!check(ruleNumber >= 0 && ruleNumber < Math.pow(2, Math.pow(2, 2*c+1)),
"Error - Rule number " + ruleNumber + " does not exist. 0 ≤ Rule number ≤ 2<sup>2<sup>2c+1</sup></sup>"))
{
/* Check for an out-of-bounds rule number. */
stopLoading();
return;
}
if (!check(startingConfigValid(startingConfig), "Error - Starting configuration invalid: " + startingConfig))
{
/* Check for an invalid starting configuration. e.g. 024930283848 */
stopLoading();
return;
}
if (!check(startingConfig.length <= size, "Error - Starting configuration length is greater than size!"))
{
stopLoading();
return;
}
if (!check(size > 0, "Error - Invalid size: " + size + ". Size > 0"))
{
/* Check for invalid size argument. */
stopLoading();
return;
}
var rule = bin(ruleNumber, Math.pow(2, 2*c+1));
$("#canvas").prop("width", size*2);
$("#canvas").prop("height", time*2);
ctx = document.getElementById("canvas").getContext("2d");
ctx.fillStyle = "#ffffff"
ctx.fillRect(0, 0, size, time);
ctx.fillStyle = "#000000"
startingConfig = padConfiguration(startingConfig, size);
/* Run the automaton. */
drawState(startingConfig, 0);
var binStrings = Array.from(Array(Math.pow(2, 2*c+1)).keys()).map(function(x) { return bin(x, 2*c+1); }).reverse();
var lastState = startingConfig;
for (var t = 1; t < time; t++)
{
var nextState = "";
for (var i = 0; i < c; i++)
{
nextState += getNewValue(rule, pad(lastState.substring(0, i+c+1), 2*c+1), c, binStrings)
}
for (var i = c; i < size-c; i++)
{
nextState += getNewValue(rule, lastState.substring(i-c, i+c+1), c, binStrings);
}
for (var i = size-c; i < size; i++)
{
nextState += getNewValue(rule, pad(lastState.substring(i-c, size), 2*c+1), c, binStrings);
}
drawState(nextState, t);
lastState = nextState;
}
stopLoading();
}
$(document).ready(function() {
$("#run").click(function()
{
startLoading();
window.setTimeout(run, 1);
});
});
|
