globals [row]  ;; this variable is the current row processed by the CA

;; the following patch variables refer to the colors of the 3 focal patches in a neighborhood
patches-own [left-pcolor center-pcolor right-pcolor] 

;; initializes the model
to setup
  ca
  set row screen-edge-y
  set (pcolor-of patch-at 0 screen-edge-y) yellow  ;; create initial black cell in the top center of the screen
end

;; runs the CA for one screenful
to go
  if (row = (- screen-edge-y)) [ stop ]  ;; stop at the last row
  ask patches with [pycor = row]
    [ do-rule ]
  set row (row - 1)
end

;; set the state of the patch below by applying rule 110
to do-rule  ;; patch procedure
  ;; assign values to patch variables based on current state of the row
  set left-pcolor pcolor-of patch-at -1 0
  set center-pcolor pcolor
  set right-pcolor pcolor-of patch-at 1 0
  ifelse ((left-pcolor = black and center-pcolor = black and right-pcolor = black) or  ;; evaluate rule 110
          (left-pcolor = yellow and center-pcolor = black and right-pcolor = black) or
          (left-pcolor = yellow and center-pcolor = yellow and right-pcolor = yellow))
    [ set pcolor-of patch-at 0 -1 black ]
    [ set pcolor-of patch-at 0 -1 yellow ]
end

;; sets up to run the next screenful (it will wrap)
to setup-continue
  ;; copy cells from the bottom of the screen to the top
  ask patches with [pycor = screen-edge-y]
    [ set pcolor (pcolor-of patch pxcor (- screen-edge-y)) ]
    
  ask patches with [pycor != screen-edge-y]  ;; clear the rest of the screen
    [ set pcolor black ]

  set row screen-edge-y  ;; reset the row to the top position
end


; *** NetLogo Model Copyright Notice ***
;
; This model was created as part of the project:
; PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN
; CLASSROOMS.  The project gratefully acknowledges the support of the
; National Science Foundation (REPP program) -- grant number REC #9814682.
;
; Copyright 2002 by Uri Wilensky.  Updated 2002.  All rights reserved.
;
; Permission to use, modify or redistribute this model is hereby granted,
; provided that both of the following requirements are followed:
; a) this copyright notice is included.
; b) this model will not be redistributed for profit without permission
;    from Uri Wilensky.
; Contact Uri Wilensky for appropriate licenses for redistribution for
; profit.
;
; To refer to this model in academic publications, please use:
; Wilensky, U. (2002).  NetLogo CA 1D Rule 110 model.
; http://ccl.northwestern.edu/netlogo/models/CA1DRule110.
; Center for Connected Learning and Computer-Based Modeling,
; Northwestern University, Evanston, IL.
;
; In other publications, please use:
; Copyright 1998 by Uri Wilensky.  All rights reserved.  See
; http://ccl.northwestern.edu/netlogo/models/CA1DRule110
; for terms of use.
;
; *** End of NetLogo Model Copyright Notice ***
@#$#@#$#@
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TEXTBOX
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Start from a\nsingle cell

TEXTBOX
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Start from the end\nof the previous run

@#$#@#$#@
WHAT IS IT?
-----------
This program models one particular one-dimensional cellular automaton -- the one known as "rule 110". A cellular automaton (aka CA) is a computational machine that performs actions based on certain rules.  It can be thought of as a "board" which is divided into cells (such as the square cells of a checkerboard). Each cell can be either on or off.  This is called the "state" of the cell. The board is initialized with some cells on and some off. A clock is then started and at each "tick" of the clock the rules are "fired" and this results in some cells turning "on" and some turning "off".

There are many kinds of cellular automata. In this model, we explore a one-dimensional CA -- the simplest type of CA. In this case of one-dimensional cellular automata, each cell checks the state of itself and its neighbors to the left and right, and then sets the cell below itself to either "on" or "off", depending upon the rule.  This is done in parallel and continues until the bottom of the board.

This model is one of a collection of 1D CA models. It is meant for the beginning user. If you have experience with CAs, we suggest you check out a more sophisticated model such as CA 1D Elementary.

In his book, "A New Kind of Science", Stephen Wolfram argues that simple computational devices such as CAs lie at the heart of nature's patterns and that CAs are a better tool than mathematical equations for the purpose of scientifically describing the world.


HOW IT WORKS
------------
As the CA computes, each patch checks the color of itself and the patches directly to the left and right of it, and then paints the patch below it according to Rule 110:

|   Y Y Y       Y Y B       Y B Y       Y B B   
|     B           Y           Y           B

|   B Y Y       B Y B       B B Y       B B B
|     Y           Y           Y           B

For example, if we have a Rule 110 CA, and the current cell is yellow and its left neighbor is black and its right neighbor is black, the cell below it is painted yellow.


HOW TO USE IT
-------------
Initialization & Running:
- SETUP initializes the model with a single cell on in the center.
- SETUP-CONTINUE copies the last row of the previous run to the top so that you can continue running the model when you click GO.
- GO begins running the model with the currently set rule. It continues until the end of the screen.


THINGS TO NOTICE
----------------
Although the rules are very simple, extremely complex patterns emerge in Rule 110.  These patterns are not highly regular nor are they completely random.

Note that the pictures generated by this model do not exactly match the pictures in Wolfram's book, "A New Kind of Science". That's because Wolfram's book computes the CA as an infinite grid while the NetLogo model "wraps" when it hits a horizontal screen boundary. To get pictures closer to the ones in the book, you may need to increase the size of the NetLogo graphics screen. You can increase the size of the screen up to the available memory on your computer. However, the larger the screen, the longer time it will take NetLogo to compute and display the results.


THINGS TO TRY
-------------
Try changing the dimensions of the graphics window either to see more of the CA's pattern or to focus in on a region of interest.

What happens to the regularity when SETUP-CONTINUE is used a number of times?  Why do you suppose that is? (Note that in this model, the CA wraps around the sides.)

Is there any consistent pattern to the way this CA evolves?

If you look at a vertical line, are there more yellow or black cells?

Can you predict what the color of the nth cell on a line will be?


EXTENDING THE MODEL
-------------------
What if you wanted to observe the behavior of a CA over many screens without having to click continue at the end of every screen? Simply replace the "stop" with "setup-continue' in the go procedure:

|  if (row = (- screen-edge-y))
|    [ stop ]

with

|  if (row = (- screen-edge-y))
|    [ setup-continue ]

What if a cell's neighborhood was five -- two to the left, itself, and two to the right?

Classical CAs use an "infinite board". The CA shown here "wraps" when it reaches the edge of the graphics screen (sometimes known as a periodic CA or CA with periodic boundary condition). How would you implement in NetLogo a CA that comes closer to the infinite board?

Try making a two-dimensional cellular automaton.  The neighborhood could be the eight cells around it, or just the cardinal cells (the cells to the right, left, above, and below).

 
RELATED MODELS
--------------
Life - an example of a two-dimensional cellular automaton
CA 1D Rule 30 - the basic rule 30 model
CA 1D Rule 30 Turtle - the basic rule 30 model implemented using turtles
CA 1D Rule 90 - the basic rule 90 model
CA 1D Rule 250 - the basic rule 250 model
CA 1D Elementary - a model that shows all 256 possible simple 1D cellular automata
CA 1D Totalistic - a model that shows all 2,187 possible 1D 3-color totalistic cellular automata. 


REFERENCES AND CREDITS
-----------------------
Thanks to Ethan Bakshy for his help with this model.

The first cellular automaton was conceived by John Von Neumann in the late 1940's for his analysis of machine reproduction under the suggestion of Stanislaw M. Ulam. It was later completed and documented by Arthur W. Burks in the 1960's. Other two-dimensional cellular automata, and particularly the game of "Life," were explored by John Conway in the 1970's. Many others have since researched CA's. In the late 1970's and 1980's Chris Langton, Tom Toffoli and Stephen Wolfram did some notable research. Wolfram classified all 256 one-dimensional two-state single-neighbor cellular automata. In his recent book, "A New Kind of Science," Wolfram presents many examples of cellular automata and argues for their fundamental importance in doing science.

See also:

Von Neumann, J. and Burks, A. W., Eds, 1966. Theory of Self-Reproducing Automata. University of Illinois Press, Champaign, IL.

Toffoli, T. 1977. Computation and construction universality of reversible cellular automata. J. Comput. Syst. Sci. 15, 213-231.

Langton, C. 1984. Self-reproduction in cellular automata. Physica D 10, 134-144

Wolfram, S. 1986. Theory and Applications of Cellular Automata: Including Selected Papers 1983-1986. World Scientific Publishing Co., Inc., River Edge, NJ.

Bar-Yam, Y. 1997. Dynamics of Complex Systems. Perseus Press. Reading, Ma.

Wolfram, S. 2002. A New Kind of Science.  Wolfram Media Inc.  Champaign, IL.
  See chapters 2 and 3 for more information on 1 Dimensional CAs
  See index for more information specifically about Rule 110.

To refer to this model in academic publications, please use: Wilensky, U. (2002).  NetLogo CA 1D Rule 110 model. http://ccl.northwestern.edu/netlogo/models/CA1DRule110. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 2002 by Uri Wilensky.  All rights reserved.  See http://ccl.northwestern.edu/netlogo/models/CA1DRule110 for terms of use.
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@#$#@#$#@
NetLogo 2.0beta4
@#$#@#$#@
setup
repeat screen-size-y - 1 [ go ]
@#$#@#$#@
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