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  • xMandelbrotViewer
    Downloads and Links xMandelbrot jar Download the standalone version of the program If Java 5 0 or higher is properly installed you should be able to run this by double clicking at least on Windows and on Mac OS 10 4 or higher On Linux if double clicking does not work you might have to right click and use Open With to open the file with Java or with a command such as java jar You can also run the program from the command line with the command java jar xMandelbrot jar Source Code Download the source code for the program as a zip archive See the README file from the download for more information Browse the source online The actual source code files can be found in the directories edu hws eck umb edu hws eck umb comp edu hws eck umb palette and edu hws eck umb util Gallery of Examples See also sample images that I made for a calendar in 2010 MandelbrotCL jar A command line version of the program which can be used to create images from settings files without a graphical user interface Documentation can be found below The source code for this program is included in the above source code links MBNetServe jar A server program that can be used to distribute the computation over a network Documentation can be found below The source code for this program is included in the above source code links Documentation for MandelbrotCL jar MandelbrotCL jar is a simple command line utility for making Mandelbrot images This program can read Mandelbrot settings files which are created by xMandelbrot jar and can create the images that are specified by those files I use this utility for example to create small thumbnail images from a group of settings files The syntax for using this command is java jar MandelbrotCL jar options filenames where filenames represents one or more settings file names and the options can include any or all or none of the following size WWWxHHH where WWW and HHH are positive integers specifies the size of the image If no size is specified 800x600 is used format XXX use XXX as the format for the image PNG is the default JPEG is also definitely supported Other formats might be supported as well onepass turn 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 specified 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

    Original URL path: http://math.hws.edu/xJava/MB/index.html (2016-02-07)
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  • Mandelbrot Examples
    produces the example This assumes that you have JavaScript enabled in your browser if not the images below will link directly to the associated settings files Any settings file can also be loaded into the program xMandelbrot jar the standalong application vesion ofthe viewer program using the Open Settings File command in the File menu of that program It can also be used with the command line program MandelbrotCL jar

    Original URL path: http://math.hws.edu/xJava/MB/MandelbrotSettings/index.html (2016-02-07)
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  • Cellular Automata and the Edge of Chaos
    computers and they can be interesting to study in their own right One type of automaton that has received a lot of attention is cellular automata For one thing they make pretty pictures For another they are related to exciting new ideas such as artificial life and the edge of chaos Here is a fairly simple example An applet showing a cellular automaton would appear here in browsers that support Java If you would like to learn more about cellualr automata here are some pages of information and Java applets that you can look at The most interesting things here are the applet on page 6 and the newer version of the same applet on page 7 which can make some awfully nice pictures such as this one 117 kilobytes About Cellular Automata Instructions for using the HandCraftCA Applet The HandCraftCA Applet The Edge of Chaos Instructions for using the EdgeOfChaosCA Applet The EdgeOfChaosCA Applet Version 2 of the EdgeOfChaosApplet for Java 1 4 or higher Bibliography The source code for the applets used on these pages is available here Java 1 4 source for Version 2 of EdgeOfChaosCA from page 7 CACanvas java a class used in SimpleCA HandCraftCA

    Original URL path: http://math.hws.edu/xJava/CA/index.html (2016-02-07)
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  • EdgeOfChaosCA, Version 2
    It runs starting from generation zero until one full image has been produced then stops The number of generations in a full image is specified when the world is first created The New Random World command creates a new world by setting each cell in the world to a randomly selected state and uses that world as the starting generation The New Random Clump creates a world in which the middle 51 cells are set to random values and the remaining cells are set to be dead The Single Dot Start command starts with a world in which the middle cell is set to state 1 and all the other cells are dead This world tends to die off quickly unless Lambda is fairly large The final command in the Control menu is Colors This command opens a dialog box that you can use to set the colors that are used to represent the different possible states that a cell can be in Several pre set palettes of colors are available and you can set an individual color by clicking on it Note that color number 0 is the color of the dead state The File menu has two commands that can be used to create new cellular automata The rules for an automaton are generated randomly but based on certain parameters that you can set The New command opens a dialog box where you can set the parameters that will be used to create the new automaton The New with Same Settings command creates a new world using the same parameters as the the current world The parameters that you can set in the New dialog are as follows the first two are the most important Number of States This is the number of different states that a cell can be in That is it is the number of different colors that can appear in the world The minimum number of states is two since you need a dead state and at least one alive state In this program the maximum number of states is 32 but this number is arbitrary Neighborhood Size When a cell decides what state to be in in the next generation it looks at its own current state and at the states of its neighbors on both sides The neighborhood size is the number of neighbors including the cell itself that are considered If the neighborhood size is 3 then the states of the cell and one neighbor on the left and one on the right are used to determine the state of the cell in the next generation If the neighborhood size is 5 then the cell two neighbors on the left and two neighbors on the right are used In this program the neighborhood size is an odd number because the neighborhood always includes the same number of neighbors on the left and on the right The larger the number of states and the bigger the neighborhood size the more rules that

    Original URL path: http://math.hws.edu/xJava/CA/EdgeOfChaosCA.html (2016-02-07)
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  • Genetic Algorithms Demo
    by two things at once An Eater can see the single square just in front of it The front is the pointy end of the T shaped Eater It can see one of four different things an Eater a plant a blank space or a wall In addition to this external information the Eater has an internal memory that contains a number between 0 and 15 This number is called the state of the Eater At each time step the Eater can perform one of the actions 1 Move forward one square 2 Move backwards one square 3 Turn in place 90 degrees to the left 4 Turn in place 90 degrees to the right It can also change its state by changing the number in its memory If it tries to move into a wall or onto a square that already contains another Eater it will not be allowed to move however it can still change its state If it moves onto a square containing a plant it eats the plant and scores a point Depending on menu settings the plant might immediately grow back somewhere else At the end of a year the fitness of the Eater is the number of plants it has eaten PLUS ONE The 1 is added to avoid having a fitness of zero Now how does an Eater decide what to do on each turn It bases its decision on two things its current state and the item that it sees in front of it Its behavior is completely determined by a set of rules that tell it what to do for each possible combination of current state and item in view All the Eater does is follow its rules The rules differ from one Eater to another In fact the Eater s rules which completely determine the behavior of the Eater make up the Eater s genetic endowment what we will call its chromosome The chromosome consists of 64 rules one for each combination of one of 16 states and one of four items in view Each rule specifies two things an action and a new state The chromosome can be considered to be just a list of 128 numbers Here is what happens at the end of a year The average fitness of the current population is computed A new population is created by making copies of the Eaters that is of the chromosomes in the current population An Eater s chance of being copied depends on its fitness Eaters that have fitness much below average are likely not to be reproduced at all although they always have some chance of reproduction Eaters with high fitness are likely to be copied several times Then a mutation operation is applied Each of the 128 numbers in each chromosome has a chance of being randomly changed This chance is 1 by default and is controlled by the Mutation Probability submenu of the World Design menu Finally a crossover operation is performed Pairs of

    Original URL path: http://math.hws.edu/xJava/GA/index.html (2016-02-07)
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  • Pentominos Puzzle Solver
    black squares and you can click Go to start solving again The Restart with Empty Board is similar but the black squares are also removed from the board The Restart with Random Board will remove all pieces from the board select a set of black squares at random and begin solving the new puzzle immediately as if you had also selected Go On a board that can be exactly filled with pentominos with no empty squares left over there is only one Restart command and it simply clears the board and waits for you to select Go Selecting Squares When selecting square to be left empty simply click on a white square to make it black You can also click on a black square to turn it back to white You can use the Go command at any time even if you have not selected the maximum allowed number of black squares A solution then means filling the white area with the largest possible number of pentominos leaving some of the white squares empty The Randomize Order of Pieces Command The program has a certain order in which it tries the pieces In this ordering the program tries the more symmetric pieces first on the grounds that the less symmetric pieces are easier to place because they come in more different reflected and rotated versions This means that on a given board you will always see exactly the same sequence of moves If you turn on the Randomize Order of Pieces option then before starting the solution the pieces are placed in a random order which will yield a different sequence of moves Note that the program would still find exactly the same solutions just in a different order This command is not available when a solution is in progress and there are pieces on the board it is available after a Restart The Check for Obvious Blocking Command Without this option you will sometimes see that the program seems to be doing something stupid You ll see an isolated group of one to four white squares that is not large enough to hold any pentomino but the program will be chugging away trying to places pieces in other parts of the board This is particularly obvious if you make a board with 3 rows and 20 columns where the problem is so bad that I have never had the patience to wait for a solution to be found This is why there is a 20 by 3 board in the Size menu rather than a 3 by 20 the 20 by 3 board is solved very quickly If you turn on the Check for Obvious Blocking option the program will check for blocking of this type every time it makes a move In fact it checks for any white area whose size is not a multiple of five or an even more complicated check when you haven t selected the maximum number of black squares This option can greatly

    Original URL path: http://math.hws.edu/xJava/PentominosSolver/index.html (2016-02-07)
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  • Chaos Game (IFS)
    Use the Show Maps menu option in the Control menu to turn off display of the maps and get a better look at the image When editing a map you can drag the corners to change the size of the map To rotate the map you can drag the arrow that is attached to the center of the map You can drag the arrows on the sides to skew the map or drag the sides themselves to change the size of the map in one direction only Finally if you click anywhere else in the map you can drag the map as a whole You can use the right mouse button or hold down the shift key when you click with the left mouse button to modify the effect of any of these edit operations If you do this while rotating the map the rotation is limited to multiples of 15 degrees If you do it while dragging the map as a whole the motion is limited to a horizontal only or vertical only motion If you modify the other edit operations the center of the map will be fixed during the operation Just try it To run the Chaos Game the following process is applied Start with a randomly selected point in the unit square Then repeat the following some specified number of times Choose one of the maps at random and move the point from its current location to the corresponding point in the chosen map Draw the dot at its final position only the final position of the dot is shown This process is repeated over and over to produce the dots that make up the image The image that is produced is a fractal that is made up of transformed and scaled copies of itself each

    Original URL path: http://math.hws.edu/xJava/IFS/index.html (2016-02-07)
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  • Maze Java Applet
    to the lower right Creating the maze is probably the most interesting part The applet is customizable using various parameters This page shows two versions created using different sizes and parameter values If your browser supported java you would see an applet here If your browser supported java you would see another applet here Click here to see the source code for this applet This applet is configurable with a

    Original URL path: http://math.hws.edu/xJava/other/maze.html (2016-02-07)
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