A (one dimensional) cellular automaton is a function1 F : Σ → Σ with the property that there is a K > 0 such that F (x)i depends only on the 2K + 1 coordinates xi−K , xi−K+1, . . . , xi−1, xi, xi+1, . . . , xi+K . A periodic point of σ is any x such that σ^p (x) = x for some p ∈ N, and a periodic point of F is any x such that F^q (x) = x for some q ∈ N. Given a cellular automaton F, a point x ∈ Σ is jointly periodic if there are p, q ∈ N such that σ^p (x) = F^q (x) = x, that is, it is a periodic point under both functions.
This project aims to explore the nature of one-dimensional Cellular Automata, in the hope of finding the structure of cellular automata through its periodic points.
License: MIT
ubuntu2004
���� 7 �
1 R S
R@
T U
V
W
X
Y
Z [
R \
0 ]
^ H _ 0 ` d H e I f I g h i
R
j k
l 0 m
n o
p
q
r s
0 t H u H v w x y
z { |
}
0 ~
0
�
z � � � N I Rule Ljava/util/HashMap; Signature ;Ljava/util/HashMap<Ljava/lang/Integer;Ljava/lang/Integer;>; <init> ()V Code LineNumberTable
createHashMap ([CI)Ljava/util/HashMap;
StackMapTable @([CI)Ljava/util/HashMap<Ljava/lang/Integer;Ljava/lang/Integer;>;
generateWords (I)Ljava/util/List; '(I)Ljava/util/List<Ljava/lang/String;>; generateWordsHelper &(Ljava/lang/String;ILjava/util/List;)V :(Ljava/lang/String;ILjava/util/List<Ljava/lang/String;>;)V applyRule #(Ljava/util/List;I)Ljava/util/List; � � K(Ljava/util/List<Ljava/lang/String;>;I)Ljava/util/List<Ljava/lang/String;>; '(Ljava/lang/String;I)Ljava/lang/String; main ([Ljava/lang/String;)V � <clinit>
SourceFile FDense.java 8 9 java/util/HashMap � � � � � � � � � � � � � java/util/ArrayList C D � � � � 2 3 BootstrapMethods � � � K � � � � � � java/lang/String java/lang/StringBuilder � � � � � � 4 5 � � java/lang/Integer � � � � � � � � @ A � � � � � � � � � � � � @1010101001010101010101010101010101010101101010101010101010101010 � � < = F K � � � � FDense java/lang/Object java/util/List java/util/Iterator [Ljava/lang/String; java/lang/Math pow (DD)D valueOf (I)Ljava/lang/Integer; (C)Ljava/lang/String; trim ()Ljava/lang/String; parseInt (Ljava/lang/String;)I put 8(Ljava/lang/Object;Ljava/lang/Object;)Ljava/lang/Object; length ()I add (Ljava/lang/Object;)Z
� � makeConcatWithConstants iterator ()Ljava/util/Iterator; hasNext ()Z next ()Ljava/lang/Object; charAt (I)C '(Ljava/lang/String;C)Ljava/lang/String; (Ljava/lang/String;I)I get &(Ljava/lang/Object;)Ljava/lang/Object; intValue append (I)Ljava/lang/StringBuilder; toString 8(Ljava/lang/String;Ljava/lang/Object;)Ljava/lang/String; size (I)Ljava/lang/Object; 8(Ljava/lang/String;Ljava/lang/String;)Ljava/lang/String; java/lang/System out Ljava/io/PrintStream; java/io/PrintStream println (Ljava/lang/Object;)V toCharArray ()[C equals (I)V � � � $java/lang/invoke/StringConcatFactory � Lookup InnerClasses �(Ljava/lang/invoke/MethodHandles$Lookup;Ljava/lang/String;Ljava/lang/invoke/MethodType;Ljava/lang/String;[Ljava/lang/Object;)Ljava/lang/invoke/CallSite; � %java/lang/invoke/MethodHandles$Lookup java/lang/invoke/MethodHandles ! 0 1
2 3
4 5 6 7 8 9 : *� � ;
< = : | =� Y� M �� �>6 � #,� *4� � �
� � W����,� ; 5 ; >
� � % 6 ?
@ A : 1 � Y�
L+� +� ; 6 B
C D : k /*� � ,*� W� > � � * � ,� ���� ; ! ( . $ >
� � 6 E F G : }
�� Y�
M*� :� ��� � :� Y� :6� �g:� d`� I� � :`� � :`� � :� � :� �� d`� F� � :`� � :� � :� � :� �� d`� C� � :� � :� � :� � :� I� � :`� � :`� � :`� � :� >� � � � � 6 � !W����,� "� W��d,� ; ~ ' ) & * / + < , @ - N . ^ / p 0 � 1 � 2 � 3 � 4 � 5 � 6 � 7 � 8 9 :! ;3 =C >U ?g @y D� E� F� +� H� I� J > 6 � H I� ! � a � P� M� E� &� H H 6 J F K : � �N6*� ��:*� d`� g*� � :*`� � :*`� � :*`� � :*`� � :*� � :�
*� d`� d*� � :*`� � :*`� � :*`� � :*� � :*� � :��*� d`� a*� � :*`� � :*`� � :*� � :*� � :*� � :�4*� d`� ^*� � :*`� � :*� � :*� � :*� � :*� � :� �*� d`� [*� � :*� � :*� � :*� � :*� � :*� � :� g*� � :*`� � :*`� � :*`� � :*`� � :*`� � :� =-� � � � # N���]-� ; � 0 P Q R S T / U @ V Q W b X s Y � Z � [ � \ � ] � ^ � _ � ` � a � b c d0 e> fL g] hj iy j� k� l� m� n� o� p� q� r� s t u* w9 xJ y[ zl {} |� �� �� Q� � > " � � } � m� j� g� d� c� L M : � �<
=>� Y�
:� Y�
:� Y�
: � $: d� $:6� % � C6� % � .� & � � & � � ' � W���̄���� (� )*:� + � ,� � (� � )66 � % � : � & � � -:
� & � .�
� -:
���� ���� (� /� ; j � � � � � � $ � * � 2 � A � P � u � { � � � � � � � � � � � � � � � � � � � � � � � � � � � > 5 � 5 N H H H � � 6� � & � � O 9 : + � � Y� � � ;
P Q �
� � � a b c