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Source code from the book "The Computational Beauty of Nature" http://mitpress.mit.edu/books/flaoh/c…
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========================================================================== CBofN C Source v2.1 --- Copyright (c) 1995--1998 --- by Gary William Flake ========================================================================== This is the README file for the example source code distribution from my book ``The Computational Beauty of Nature,'' hereafter abbreviated as CBofN. As a shameless sales plug, CBofN is about how nature can be appreciated in terms of simple computational processes. The book is in five parts (Computation, Fractals, Chaos, Complex Systems, and Adaptation) and explains each topic in terms of the others. The source code in this distribution contains many simple example programs of each topic. Unlike most other books dealing with these topics, every single image contained in CBofN can be duplicated by the reader with these programs. All of the code is written in C and should compile on most any platform. I have personally compiled it under Solaris, Linux, and Windows 98. Each program is command-line driven, so you only need to compile the program once to do 99.9% of what they can do. You may also find the programs surprisingly powerful given their relatively small sizes. Moreover, all of the examples are verbosely documented, so they should be easy to modify. In fact, the man pages are automagically generated from the C source files with a Perl script. You may use the source code for any purpose according to the standard GNU "copyleft" agreement (also contained in this distribution) as long as you neither remove nor modify my comments in the code. Anything else goes. Of course, there is no warranty for the code, so if your computer reaches some sort of semi-conscious state, it ain't my fault. This README is divided into three more sections. The first section has information on how to get a pristine copy of the software distribution as well as how to get a copy of CBofN. The second section contains a brief summary of all of the programs organized by the book part from which the examples come from. The final section explains some of the programming issues involved in producing these examples and will give you some hints if you want to expand on the programs. NEWS: Look in cbn/code/cbn98/README in the distribution for information specific to the Windows port. Enjoy! -- GWF ============================================ Getting the Source Code of CBofN (and CBofN) ============================================ The home website for CBofN is located at https://mitpress.mit.edu/sites/default/files/titles/content/cbnhtml/home.html Inside the main page there is a link leading to the source code section. Follow this link. In the the source code section there are many options for downloading various source code distributions and precompiled binaries. To get a copy of CBofN, check out the ordering information section from the URL above. ================ Program Overview ================ Programs that have graphical output can produce either raw points, PostScript, PPM, or plot to an X window, Linux VGA, Windows, or Mac device. See the ``Programming Issues'' for how the plotting methods can be expanded. Computation ----------- * STUTTER - a simple lisp interpreter that only understands car, cdr, cons, if, set, equal, quote, and lambda, but is still Turing-complete. Uses stop-and-copy garbage collection and has an adjustable heap size. Examples that implement integer and floating-point arithmetic are provided. There is even an example STUTTER function to compute the square root of a floating-point argument with nothing but the primitives listed above. Fractals -------- * DIFFUSE - diffussion limited aggregate growth that looks like coral. * LSYS - builds L-systems fractals. Accepts multiple rules so that complicated fractals (such as a Penrose tiling) can be expressed. Great for generating plant-like fractals. * MRCM - uses the Multiple Reduction Copy Machine algorithm to generate affine fractals. Excepts an arbitrary number of transformations. Good for making snowflakes and mosaic patterns. * IFS - similar to MRCM but uses Iterated Function Systems for finer granularity. * MANDEL - plot the famous Mandelbrot set. There are options for the displayed coordinates, zoom level, coloring schemes, etc. * JULIA - generates Julia sets, which are related to the Mandelbrot set and has options similar to MANDEL. Chaos ----- * GEN1D - generate a time series from a one-dimensional map. Nothing fancy; it just shows how chaos can be seen in simple systems. * BIFUR1D - plot a bifurcation diagram for a one-dimensional map to illustrate how a change in a single parameter can move a system from fixed-point behavior, to periodic, and finally to chaos. Different regions can be zoomed in on. * PHASE1D - plot the phase-space and trajectories of a one-dimensional map. Showing trajectories in the phase space more clearly illustrates why fixed-points and limit cycles occur. This can also be used to show the exponential divergence of nearby trajectories. * HENON - plot the phase space of the Henon map, a two-dimensional system with a fractal shape. Different regions can be zoomed in on. * HENBIF - plot a bifurcation diagram for the Henon system. This is similar to BIFUR1D but shows that bifurcations apply to multidimensional systems as well. * HENWARP - takes a square of a specified area and ``warps'' it a fixed number of times by the Henon system. This illustrates the stretching and folding motion of chaotic systems as well as shows how points within an attractor's basin of attraction are eventually forced into a strange attractor. * LORENZ - plot the phase space of the Lorenz system, a three-dimensional system described by differential equations with a fractal shape. Both plain state space plots and delayed state space plots are possible. * MG -plot a two-dimensional embedding of the phase space of the Mackey-Glass system, a delay differential system, with arbitrary parameters. * ROSSLER - similar to LORENZ, but uses the Rossler system. * GSW - the time evolution of an individual-based three species predator-prey ecosystem is simulated according to the specified parameters. The three species consist of plants, herbivores, and carnivores (grass, sheep, and wolves; hence the name GSW). Updates are done synchronously, and each species has several parameters which can control the life cycle, from the ability to give birth, to the likelihood of starvation. Population statistics of the three species can be calculated over a subset of the entire grid. * PREDPREY - plot the phase space of a three species predator-prey system, a three-dimensional system described by differential equations and with a fractal shape. Both plain state space plots and delayed state space plots are possible. * LOTKA - integrate the two-species Lotka-Volterra predator-prey system with the second-order Euler's method. This program serves as a simple introduction to differential equations. * HENCON - control the Henon system with the OGY control law for arbitrary choices of the system parameters. The control law is analytically calculated based on the system parameters. The user can select times in which control is turned on and off so that time-to-control and transients can be observed. Gaussian noise can also be injected into the system. Complex Systems --------------- * CA - simulate arbitrary one-dimensional cellular automata with an arbitrary choice of simulation parameters. Random rules can be generated and used with a desired lambda value. * LIFE - simulate Conway's Game of Life with an arbitrary set of initial conditions. Input files need to be in the PBM file format. * HP - simulate and plot the time evolution of the hodgepodge machine according to specified parameters. With a proper choice of parameters, this system resembles the Belousov-Zhabotinsky reaction which forms self-perpetuating spirals in a lattice. * TERMITES - Simulate a population of termites which do a random walk while possibly carrying a wood chip. Under normal circumstances, the termites will self-organize and move the wood chips into piles without a global leader. The termites' behavior is dictated by the following set of rules: If a termite is not carrying anything and she bumps into a chip, then she picks it up, reverses direction, and continues with the random walk. If she is carrying a chip and bumps into another, she drops her chip, turns around, and starts walking again. Otherwise, she just does a random walk whether she is carrying a chip or not. * VANTS - simulate and plot a population of generalized virtual ants (vants). The behavior of the vants is determined by a bit string with length equal to the number of states that each cell in the vants' grid world can take. If a vant walks on a cell in state S, then the vant turns right if the S'th bit of the rule string is 1 and left if it's 0. As it leaves the cell the vant changes the state of the old cell to (S + 1) % (number of states). * BOIDS - simulate a flock of boids according to rules that determine their individual behaviors as well as the ``physics'' of their universe. A boid greedily attempts to apply four rules with respect to its neighbors: it wants to fly in the same direction, be in the center of the local cluster of boids, avoid collisions with boids too close, and maintain a clear view ahead by skirting around others that block its view. Changing these rules can make the boids behave like birds, gnats, bees, fish, or magnetic particles. See the RULES section of the manual pages for more details. * SIPD - the spatial iterated Prisoner's Dilemma is simulated and plotted over time according to the specified parameters. Each cell in a grid plays a specific strategy against its eight neighbors for several rounds. At the end of the last round, each cell copies the strategy of its most succesful neighbor, which is then used for the next time step. Possible strategies include 'Always Cooperate,' 'Always Defect,' 'Random,' 'Pavlov,' and 'Tit-for-Tat.' * EIPD - the ecological iterated Prisoner's Dilemma is simulated over time according to the specified parameters. At every time step the population of each strategy is calculated as a function of the expected scores earned against all strategies weighted by the populations of the opponents. Possible strategies include 'Always Cooperate,' 'Always Defect,' 'Random,' 'Pavlov,' and 'Tit-for-Tat.' * ASSOC - attempt to reconstruct a potentially corrupted image with a McCulloch-Pitts feedback neural network that acts as an associative memory. The weights of the network are determined via Hebb's rule after reading in multiple patterns. Weights can be pruned either by size, locality, or randomly. * HOPFIELD - solve a task assignment problem via a Hopfield neural network while plotting the activations of the neurons over time. The program uses the K-out-of-N rule for setting the external inputs and synapse strength of the neurons. Adaptation ---------- * GASTRING - use a genetic algorithm to breed strings that match a user-specified target string. This program illustrates how GAs can perform a type of stochastic search in a space of discrete objects. Reproduction of strings entails crossover and mutation with strings being selected based on fitness. * GABUMP - use a genetic algorithm to find the maximum of a single-humped function that is centered at a user-specified location. This program serves as an example of how GAs can be used to optimize functions which take a floating point argument. Reproduction of strings entails crossover and mutation with strings being selected based on fitness. * GASURF - use a genetic algorithm to find the maximum of a multi-humped function. This program serves as an example of how GAs can be used to optimize function which take a multiple floating point arguments. Reproduction of strings entails crossover and mutation with strings being selected based on fitness. * GATASK - use a genetic algorithm to solve a task assignment problem with user-specified costs. This program illustrates how GAs can perform combinatorial optimization. Reproduction of strings entails special crossover and mutation operations which preserve constraints on the form of feasible solutions with strings being selected based on fitness. * GAIPD - use a genetic algorithm to evolve IPD strategies according to user-specified constraints. This program illustrates how GAs can demonstrate co-evolution since IPD strategies can only be successful within the context of their likely opponents. Reproduction of strategies entails crossover and mutation with strategies being selected based on fitness. * ZCS - train a zeroth level classifier system (ZCS) to traverse a two-dimensional terrain, avoid obstacles, and find food with the implicit bucket brigade algorithm and a genetic algorithm. At the beginning of each step the ZCS is placed at a random location of it's world. It interacts with its environment until it finds food, which yields a reward. The simulation then restarts with the ZCS placed at a new random location. The progress of the ZCS is continuously plotted, while the statistics on the time to find food are calculated and displayed. At the end of the simulation the classifiers that make up the final ZCS are saved to a log file. * ZCSCUP - train a zeroth level classifier system (ZCS) to solve the cups problem with the implicit bucket brigade algorithm and a genetic algorithm. Solving this problem requires the ZCS to learn to remember important features from previous states, which makes this problem very challenging. The ZCS always starts in the same initial position. It interacts with its environment until it finds both cups, which (only at that point) yields a reward. The simulation then restarts with the ZCS placed at the original location. The progress of the ZCS is continuously plotted, while the statistics on the time to find both cups are calculated and displayed. At the end of the simulation the classifiers that make up the final ZCS are saved to a log file. * MLP - train a multilayer perceptron with a single hidden layer of neurons on a set of data contained in a file using the backpropagation learning algorithm with momentum. Output units can be linear or sigmoidal, allowing you to model both discrete and continuous output target values. ================== Programming Issues ================== This section briefly describes the programming philosophy that I've been operating under while producing this source code. As such, the following is mostly irrelevant to the casual user, but may be helpful to those who wish to hack the code. My primary goal while producing this code has been to make it short and sweet. I wanted each program to be comprehensible to others but to also illustrate something useful. And since I wanted every image in my book to be reproducible by the reader, the programs had to be strong enough to do some non-trivial things. With this in mind, what follows are the basic programming guidelines that I've followed. Note that these are somewhat in conflict with what most professional hackers would consider good programming practices. I make no apologies for having deviated from the usual heuristics other than to say that I had my reasons. Input Interface - completely command-line driven with many options. Thus, I have no GUIs to make the code non-portable. The command-line parser is easily understood by others and allows for long option names. Thus, there is no need to link to third-party libraries. Moreover, the source code can be parsed by a Perl script to extract the options section for man pages. Output Interface - for graphics, I use a simple and generic plotting interface that maps well into virtually any known plotting technology. My plot routines only know how to plot dots and lines and to handle simple scaling of coordinates and colors. The flip side to this is that adding drivers is simple. Currently, I have drivers for X11, PostScript, PGM, raw, Linux VGA, and Windows. Non-graphical output usually goes to the standard output. In some cases, the reader may wish to use another third-party program to plot the numerical output. Globals - I use them to avoid excessive parameter passing. Exception Handling - almost none. If you give a command-line option a nonsense value, a program may very well core dump. So it goes. Adding nice error checks would have bloated the code considerably. Documentation - self extracting and overly verbose. All programs have a detailed comment at the beginning that gives an overview of the code. Every significant subroutine is documented. I've also taken great pains to explain any hackery that is non-trivial. The man pages are generated from a Perl script that grabs the initial header comment, the command-line options structure, and the help string. Moreover, the header comment has a section entitled "NOTES" that does not appear in the man page and only serves to help those perusing the source code. Reuse - all programs link to a library named libmisc.a that contains many routines that are used by multiple programs. Included in this are the plotting routines, the command-line parser, a simple text scanner for parsing data files, code to read PBM files, and other miscellany. Modifying the code for your own use should be relatively easy. Here are some examples of what you may wish to do: 1. Add a new plotting driver - See pgmplot.c or psplot.c for examples of how to write the drivers. You only need to define four functions that initialize the driver, plot a point, plot a line, and finish the plot. Afterwards, the plot_init() function in plot.c needs to have a little section of code added to tell the rest of the routines how to access the new driver. 2. Add a feature - For example, you could add options to save and restore network weights in mlp.c. Use the scanning routines to parse the output file. Or, you could add another one-dimensional map to the chaos programs. 3. Adapt the code - The source in zcscup.c is actually a modified version of zcs.c altered for a very specific task. You could similarly modify other programs as well. 4. Experiment with variations - some of the programs are highly experimental in that there are no "correct" implementations. For example, you could improve on gsw.c by adding some simple AI to the animals. 5. Just use libmisc.a - you may also use the routines in the common library for other tasks unrelated to the programs in this distribution. Regardless of how deep you dive into the source code, I hope you enjoy the programs. Happy hacking! -- GWF ==========================================================================