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  • subpixel sampling off If this option is omitted subpixel sampling is used This is an option in the Control menu of xMandelbrot jar subpixel sampling can produce smoother more attractive images in many cases net XXX add one or more network workers The format for XXX is a list of one or more hosts separated by commas Each host can be specifed as a host name or IP address optionally followed by a colon and a port number The port number is only necessary if different from the default 17071 No spaces are allowed in the list of computers A copy of MBNetServe jar should already be running on each of the specified computers For example to make small JPEG images for two files named mbdata1 xml and mbdata2 xml java jar MandelbrotCL jar size 160x120 format jpeg mbdata1 xml mbdata2 xml By the way if you are working with very large images you might need to tell the java virtual machine to use more memory than it ordinarily would You can do this with the Xmx option to the java command For example java jar Xmx2000m MandelbrotCL jar size 3300x2550 settings xml The program has been used for images as large as 10800 by 7200 pixels About networking It can take a long time to compute some Mandelbrot images This is especially true for high precision computation which is used when you zoom in so far that the standard Java real number implementation does not have enough significant digits to represent the numbers involved The networking option is for people who want to speed up these long computations and who have access to several networked computers To distribute Mandelbrot computations over a network you must run MBNetServe jar on each computer EXCEPT the one where you will run xMandlebrot jar or MandelbrotCL jar Once that is done you can use the Configure Multiprocessing command in the Control menu of xMandelbrot to configure that program to use the network For MandelbrotCL use the net option You will need to know something about networking in order to use this option Most important you will need to know the host names or IP addresses of the computers where the server is running To run MBNetServe jar on the computers that you want to use as computation servers use the following command in the directory that contains the program java jar MBNetServe jar options where the options can include processcount XXX use XXX processes instead of the default number Enter 0 for XXX to use one process for each available processor The default is to use one less than this if the number of processors is greater than one timeout XXX exit after XXX minutes of inactivity The default is 30 minutes Use 0 for XXX to mean that there is no timeout You can also stop the server by pressing Control C in the window where the program is running once accept one connection and exit when that connection is closed The

    Original URL path: http://math.hws.edu/xJava/MB/xMandelbrotSource-1-2/README.txt (2016-02-07)
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  • About Cellular Automata
    compute a new generation of cells An applet demonstrating how a cellular automaton works would appear here in browsers that support Java Click to compute the New World This applet shows a two state automaton in which a cell can be either black or white Each cell has three neighbors counting itself The rules for this CA say that if all three of these cells are white then the new state of the cell will be white if all three of the cells are black then the new state of the cell will also be white in any other case the new state of the cell will be black As the applet animation runs the three cells that are being considered are framed in blue In the New World the cell that is being computed is also framed in blue After states have been computed for all the cells the states in The World are replaced by the states in the New World This operation can then be repeated over and over to produce suceeding generations of cells In fact when CA s are displayed they are not usually shown as a single row of cells that changes with time Instead the second gernation of cells is drawn under the first then the third generation is drawn under the second and so on This produces a potentially very nice two dimensional pictures in which you see the whole evolution of the CA through time This is what is done for the CA on the index page which uses the same rules as the CA in the above demonstration I find it surprising that such simple rules can produce such complicated and interesting patterns A nice way to visualize the rules of a CA is to show a cell and its

    Original URL path: http://math.hws.edu/xJava/CA/CA.html (2016-02-07)
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  • Instructions for HandCraftCA Applet
    is a rectangle showing a cellular automaton that uses those rules When the applet starts up an initial world is created and shown at the top of the rectangle The cells in this world are assingned states at random The cells are quite small each one occupies a single pixel The CA simply runs continuously computing new generations of the world and displaying them When you change one of the rules the change will affect the next generation and the generations that come after that Previous generations will not be recomputed however Big cell CA Below the rules on the left is a rectangle showing several generations of another CA which uses the same rule In this case the cells are rather large so you can see them better individually Again the first generation of cells is created at random and displayed at the top of the rectangle The next few generations are displayed below it but just enough to fill the rectangle When you change a rule all the generations are recomputed and redisplayed immediately You can also change the state of one of the cells at the top of this rectangle Just click on the cell you want to change Any resulting changes in later generations are computed and displayed Try pointing the mouse at one of the cells below the first row That cell and the three cells above it will be outlined in yellow The three outlined cells in the row above are the ones that were used to compute the state of the cell that you are pointing at Furthermore in the rules panel the rule that was used to compute the state of the cell will also be hilited This might help you understand how the computation was done It can also help you

    Original URL path: http://math.hws.edu/xJava/CA/AboutHandCraftCA.html (2016-02-07)
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  • Hand-crafting a Cellular Automaton
    if you have not already read it An applet for creating cellular automata would appear here in browsers that support Java Index Previous Next EdgeOfChaos Applet Version 1 EdgeOfChaos Applet Version 2 Eck s Java Page David J Eck Department

    Original URL path: http://math.hws.edu/xJava/CA/HandCraftCA.html (2016-02-07)
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  • Introduction to the Edge of Chaos
    their behavior seems for all intents and purposes to be random Langton called such CA s chaotic Their behavior is boring because it is completely unpredictable and can only be described as a mass of unrelated details But some CA s display interesting complex almost lifelike behavior Langton said that these CA s are near the border between order and chaos If they were more ordered they would be too predictable to be interesting if they were less ordered they would be too chaotic Langton defined a simple number that can be used to help predict whether a given CA will fall in the ordered realm in the chaotic realm or near the boundary on the edge of chaos The number can be computed from the rules of the CA It is simply the fraction of rules in which the new state of the cell is living The rule in which a cell and all its neigbors are dead is not counted since Langton assumed that the new state in this rule is always death He called this parameter lambda The lambda parameter of a CA is a number between 0 and 1 If lambda is 0 then all cells die immediately since every rule leads to death If lambda is 1 then any cell that has at least one living neighbor will stay alive in the next generation and in fact forever More generally values of lambda close to zero give CA s in the ordered realm Values close to 1 give CA s in the chaotic realm The edge of chaos is somewhere in between Unfortunately we can t simply say that there is a value of lambda that represents the edge of chaos It s more complicated than that Here is what Langton found Suppose you start

    Original URL path: http://math.hws.edu/xJava/CA/EdgeOfChaos.html (2016-02-07)
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  • The EdgeOfChaosCA Applet
    also comes in an application version that can save images and files The new version is on the next page see that page for more information For information about this applet and instructions for using it please see the instructions page if you have not already read it An applet for creating cellular automata would appear here in browsers that support Java Index Previous Next HandCraftCA Applet Eck s Java

    Original URL path: http://math.hws.edu/xJava/CA/EdgeOfChaosCA1.html (2016-02-07)
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  • Bibliography: Cellular Automata and the Edge of Chaos
    The edge of chaos is a central idea Stuart Kauffman At Home in the Universe The Search for Laws of Self organization and Complexity Oxford University Press 1995 Kaufmann explains his ideas about how various forms of complexity including life itself can arise from simple rules The Edge Of Chaos idea plays a large role in his thinking Christopher Langton Computation at the Edge of Chaos Phase Transitions and Emergent

    Original URL path: http://math.hws.edu/xJava/CA/bibliography.html (2016-02-07)
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  • Index of /xJava/CA/EdgeOfChaosCA_source
    This directory and the subdirectory xca contain the Java source code for version 2 01 of EdgeOfChaosCA This version requires Java 1 4 or higher Version 2 01 September 2006 fixes a problem with scrolling of the image under Mac OS The file compile sh contains the commands needed to compile the source code and to build a jar file containing the program The commands as give work on Linux

    Original URL path: http://math.hws.edu/xJava/CA/EdgeOfChaosCA_source/ (2016-02-07)
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