The programs below are listed in the order in which they appear
in the text.
interprets simple lisp and 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.
Generates diffusion limited aggregate growth that looks like coral.
L-system fractals. Accepts multiple rules so that complicated
fractals (such as a Penrose tiling) can be expressed. Great for
generating plantlike fractals.
mrcm Uses the
Multiple Reduction Copy Machine algorithm to generate affine fractals.
Accepts an arbitrary number of transformations. Good for making
snowflakes and mosaic patterns.
ifs Similar to
mrcm but uses Iterated Functional Systems for finer
the famous Mandelbrot set. There are options for the displayed
coordinates, zoom level, coloring schemes, etc.
Generates Julia sets, which are related to the Mandelbrot set. Has
options similar to mandel.
Generates a time series from a one-dimensional map. Nothing fancy; it
just shows how chaos can be seen in simple systems.
Plots 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.
Plots 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.
the phase space of the Hénon map, a two-dimensional system with a
fractal shape. Different regions can be zoomed in on.
a bifurcation diagram for the Hénon system. This is similar to
bifur1d but shows that bifurcations apply to multidimensional
systems as well.
Takes a square of a specified area and ``warps'' it a fixed number of
times by the Hénon 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
the phase space of the Lorenz system, a three-dimensional system
described by differential equations with a fractal shape. Both plain
phase-space plots and delayed state-space plots are possible.
Similar to lorenz, but uses the Rossler system.
mg Plots a
two-dimensional embedding of the phase space of the Mackey-Glass
system, a delay-differential system, with arbitrary parameters.
gsw Simulates an
individual-based three-species predator-prey ecosystem 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 their life cycles, 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
Plots the phase space of a three-species predator-prey system
(described by differential equations) which may be fractal in shape.
Both plain phase-space plots and delayed state-space plots are
Simulates the two-species Lotka-Volterra predator-prey system with a
second-order Euler's method. This program serves as a simple
introduction to differential equations.
Controls the Hénon 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 be injected into the
arbitrary one-dimensional cellular automata with an arbitrary choice
of simulation parameters. Random rules can be generated and used with
a desired lambda value.
Conway's Game of Life with an arbitrary set of initial conditions.
Input files need to be in the PBM file format.
hp Simulates and
plots 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.
Simulates 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 it bumps into
a chip, then it picks it up, reverses direction, and continues with
the random walk. If it is carrying a chip and bumps into another, it
drops the chip, turns around, and starts walking again. Otherwise, it
just does a random walk whether it is carrying a chip or not.
Simulates and plots 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 is 0. As it leaves the cell the vant changes the state of the old
cell to (s + 1) modulo the number of states.
Simulates 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.
and plots the spatial iterated Prisoner's Dilemma 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
successful neighbor, which is then used for the next time step.
Possible strategies include ``Always-Cooperate,'' ``Always-Defect'',
``Random,'' ``Pavlov,'' and ``Tit-for-Tat.''
the ecological iterated Prisoner's Dilemma 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.''
to reconstruct a 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, by locality, or
Solves 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.
Uses 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 Uses 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
gasurf Uses 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
functions which take multiple floating-point arguments.
gatask Uses 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.
gaipd Uses a
genetic algorithm to evolve iterated Prisoner's Dilemma (IPD)
strategies according to user-specified constraints. This program
illustrates how GAs can demonstrate coevolution since IPD strategies
can only be successful within the context of their likely opponents.
zcs Adapts a
zeroth level classifier system (ZCS) with the implicit bucket brigade
algorithm and a genetic algorithm so that the ZCS can traverse a
two-dimensional terrain, avoid obstacles, and find food. At the
beginning of each step the ZCS is placed at a random location of its
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.
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 Trains 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