Fractal Science Kit
The Fractal Science Kit fractal generator is a Windows program to generate a mathematical object called a fractal. The term fractal was coined by Benoit Mandelbrot in 1975 in his book Fractals: Form, Chance, and Dimension. In 1979, while studying the Julia set, Mandelbrot discovered what is now called the Mandelbrot set and inspired a generation of mathematicians and computer programmers in the study of fractals and fractal geometry.
Like
other mathematical ideas, fractals involve numbers and equations. Unlike most
other mathematical ideas, fractals can be used to generate complex, beautiful images that
appeal to mathematicians and children alike. Swirling spirals, endless
self-similar repetitions receding into the distance, geometric objects arranged
in infinitely complex patterns, plant-like creations, geologic designs, clouds,
and more, comprise the fractal landscape. These wondrous patterns defy logic yet
owe their very existence to mathematics and computers. See the
Fractal Image Gallery
for some examples of the myriad of fractal designs possible.
A
fractal image is created by evaluating a complex equation or by performing a
sequence of instructions, and feeding the results back into the equation over
and over again. During the iteration, you accumulate statistics and map the
resulting data to colors, creating the fractal image. By varying the equation or
the instructions, you can create Mandelbrot Fractals,
Orbital Fractals,
L-System Fractals, Orbit Traps,
and more.
The Fractal Science Kit
fractal generator provides a rich framework for exploring the world of
fractals. It handles the common processing steps required to generate a fractal
image so that you can concentrate on the fun part; developing the fractal
formulas/equations,
complex transformations, and coloring schemes that define the fractal.
This
is not to say that you must write code to use the Fractal Science Kit. On the
contrary, hundreds of
Built-in Programs are available right out of the box and most of
these provide options that yield countless variations. A fractal image is the
result of combining an equation with data collection programs, complex transformations, and
color controllers (the instructions that map the data to colors). By choosing
different combinations of these programs/options, you
can generate more fractal images than you could ever hope to view in your
lifetime without ever writing a single line of code.
The Fractal Science Kit
fractal generator supports
many different
Fractal Types including:
Mandelbrot, Julia,
Convergent,
Newton, Orbit Traps,
Sierpinski Triangle, IFS,
Strange Attractors, Rep-N
Tiles, Symmetric Icons, Symmetric Attractors,
Frieze Group Attractors,
Wallpaper Group Attractors,
Hyperbolic Attractors,
Apollonian Gasket, Circle
Inversion, Schottky Group, Kleinian Group, L-System
and many more. Hundreds of built-in equations, transformations, orbit traps, and
color controllers, allow the casual user to produce stunning fractal images
while providing the experienced fractal developer a rich set of illustrative
examples on which to build his/her own fractal programs.
The Fractal Science Kit
fractal generator provides an
interactive programming environment with
Application Windows for viewing the fractal
image, modifying the properties that define the fractal, examining the data
behind the fractal, and viewing/editing the fractal programs, macros (inline
functions/methods), and color gradients, used by the Fractal Science Kit to produce the final image.
The Properties Pages allow you to view/edit all the properties associated with a fractal.
Properties control every aspect of the resulting fractal image and the Fractal
Science Kit fractal generator supports a rich set of properties for choosing colors, controlling
image processing tasks (e.g., smoothing,
sharpening, embossing, anti-aliasing), controlling Data
Normalization (e.g., contrast stretching, histogram equalization, data
scaling via a transfer function), selecting/editing the Fractal Programs
(equations, data collection programs, transformations, and color controllers), and much more.
The
Programming Language you use to develop your Fractal Programs, supports
a complete set of control structures including if statements,
while
loops, for loops, switch statements, inline functions/methods, arrays, and user
defined objects. The complex data type is the fundamental variable type, and
arithmetic operators and functions handle complex operands/arguments. A rich set
of built-in functions/methods are included, and you can develop your own library
of functions/methods for use throughout the application.
Programs written using the L-System Language are also supported.
This documentation describes what you need to know to use the
Fractal Science Kit fractal generator effectively. This document does not describe the hundreds of
Built-in Programs
that define the fractal formulas, orbit traps, transformations, and color
controllers, that can be combined to produce countless fractals right out of the
box. These are described in the
comment section at the
beginning of each program. This document does describe the structure of these
programs, how these programs are hooked into the application framework, the programming
language used to develop your fractal programs, and the built-in tools available to help
you along the way.
Documentation Roadmap
See the Product Overview for a more
detailed overview of the Fractal Science Kit fractal generator or delve right into the
product documentation
using the links on the left. For a complete list of topics, view the
Site Map.
After you download the application, see Getting Started for tips on what to do next.
The different Fractal Types are explained in the sections on Mandelbrot Fractals, Orbital Fractals, and L-System Fractals. Each section describes the basic framework for fractal generation processing with respect to fractals of the given type.
The Fractal Science Kit Mandelbrot Fractals encompass several related types including Mandelbrot fractals, Julia fractals, Convergent fractals, Newton fractals, and Orbit Traps. Orbit Traps can also be used to produce Circle Inversion, Apollonian Gasket, Schottky Group, and Kleinian Group fractals. The Sierpinski Triangle, Sierpinski N-gons, IFS (Iterated Function System) fractals, Strange Attractors, Rep-N Tiles, Circle Inversion fractals, Kleinian Group fractals, Symmetric Icons, Symmetric Attractors, Frieze Group Attractors, Wallpaper Group Attractors, and Hyperbolic Attractors, are all examples of the Fractal Science Kit Orbital Fractals. Lindenmayer System Fractals or L-System Fractals can be viewed as a stand-alone fractal or used to define L-System based Orbit Traps.
The
Application Windows and
Properties Pages sections, discuss each of the
application's windows in detail and document all of the
properties used to control the fractal generation framework.
The Fractal Science Kit fractal generator comes with hundreds of Built-in Programs which are used to create your fractals. In addition, you can develop your own Fractal Programs to define the Equations, Data Collection Programs, Color Controllers, and Complex Transformations that generate the fractal image.
The set of statements that make up a
Fractal Program are called
Program Instructions or Instructions for short.
Instructions are written in a language that is similar to the C programming
language. See
the
Programming Language section for a complete description of
the Syntax of the programming language.
The Built-in Functions and Built-in Macros are a set of built-in functions/methods available to all your fractal programs. You can also develop a library of your own Macros; i.e., Objects, Inline Functions, Inline Methods, and #Define Statements for use throughout the application.
The
Built-in Programs
are based on the work of many others. The Fractal
Links list the most important sources for ideas but additional
inspiration was found throughout the Internet on pages devoted to fractals and/or mathematics. I have
tried to credit the ideas behind each program in the
comment section at the
beginning of the program. The more than 40,000 lines of source code for the built-in fractal programs and the built-in macros (inline
functions/methods) are accessible via the Program
Browser and Macro Editor, respectively.
When you're ready to begin using the Fractal
Science Kit fractal generator, a
set of in-depth
Tutorials help you learn how to generate Mandelbrot Fractals,
Orbit Traps,
Orbital Fractals, and
L-System Fractals. In addition to covering the basic
concepts, these tutorials explain how you can use complex transformations and
color controllers to take control of every aspect of the fractal image
processing. A
Fractal Programming tutorial introduces
you to the key concepts involved in writing your own fractal programs.
Finally, a downloadable collection of illustrative Fractal Examples are available to get you started quickly. Each of the examples generates a base fractal and the online description includes experiments to illustrate key concepts that you can use to produce hundreds of variations.
Download the 30-day evaluation copy of the Fractal Science Kit fractal generator today!
Also, check out my deviantART gallery. The gallery contains a collection of fractals I have generated with the Fractal Science Kit fractal generator. You can also join me on Facebook, Flickr, or MySpace.
I hope that you find the Fractal Science Kit fractal generator useful in your quest to understand these extraordinary and beautiful mathematical creations. Enjoy!
Ross Hilbert
hilbert@fractalsciencekit.com