KDE Turtle - fractal generation through repetitive rule substitution

Version 0.1, 23 September 1997

Index

Introduction
Turtle
Examples
Graphical User Interface
Installation
Bugs
Changes
Acknowledgements
Copyright

Introduction

This application can be used to generate visual representations of fractals described by an axiom and a rule set to be expanded to a certain level through repeated rule substitutions into the axiom and making the result the axiom for the next level. The axiom and rules possibly ( and most likely if it is to be of any use ) contains embedded commands which is understood by a turtle which will draw them on a visual pane.

Turtle

The turtle currently understands the following commands ( which are open to suggestions BTW )

F - move and draw 1 unit forward
B - move and draw 1 unit backwards
- - turn 1 arc anti-clockwise
+ - turn 1 arc clockwise
< - decrease unit length
> - increase unit length
[ - push turtle state onto stack ( unit length, direction, position )
] - pop state from stack restoring to exact state as it was with last push

The turtle first renders the fractal in imaginary space and then uses the result to calculate a scalar by which to scale all the initial values ( unit length, unit in/decremental, start position ) and then renders again onto a visual canvas. It uses an iterative approach ( in stead of a possible recursive approach ) which results in increased speed however accompanied by greater memory requirements ( +- 256 KB for fine grained result ) An example of a possible session might be best described by the well known Koch fractal. In this case the starting axiom is F and there is only one rule FF-F++F-F. The rule syntax is simply a character signaling which character in the axiom to replace with the rule followed by the replacement string. Thus, in this case F will be replaced by F-F++F-F. This means that at level 0 ( first substitution of rule into axiom ), the result is

F-F++F-F

At level 1 we get as result

F-F++F-F-F-F++F-F++F-F++F-F-F-F++F-F

It should be pretty clear that this kind of expansion could result in pretty rappid growth of the fractal. Level 2 ( which i'm not going to write down here or anywhere for that matter ) results in

Eventually we end with something like

which is the application's representation of the memory limited maximum expansion through iterative approach. There are quite a few well known fractals of this kind ( of which some are included in the distribution ) and you should play with them. The real challenge however is to create one's own which is easier said ( or typed ) than done. If you create a nice authentic one, you can send it to me and i will include it in future distributions with appropriate acknowledgement.

Examples

Following are a couple of examples to try out. They should be available in .tur files in the archive this application was distributed by. Here they are presented presented in the following way

Description

Try them out.

Simple plant

Simple plant

Nice tree

A Xmas tree

Stylish tree

The dragon curve

Grass in the wind

Another branching pattern

Hexagonal structure

Hilberts space-filling curve

The quadratic Koch island

Segment of Koch's snow flake. A classic fractal example

Example for iteration: This fractal grows only linearly.

Peano's space filling curve

Graphical User Interface

The user interface attempts to be straight forward. A couple of popup menus provides access to the functionality of the application

File

New - reset axiom, rules, level and direction count
Load - load a fractal description ( .tur files )
Save - save fractal description for later use
Print - print fractal
Bitmap - save fractal image as .bmp file
Quit - you don't want to use this

Edit

Edit - edit the fractals axiom, rules and direction count. The rules should be entered 1 per line where the first character indicates which character the rule will replace during rule substitution and the rest of the characters up to the end of the line is the rule and will replace the character during expansion. The directions indicates into how many equil arcs should the 360 degree revolution be divided e.g. direction 4, axiom F and single rule F-F-F-F will draw a rectangle as 360/4=90 degrees

View

Next Level - render the next rule substitution session of the fractal
Level 1 - 15 - render a specific level of rule replacement
Last Level - render the maximum possible level given the fixed ceiling amount of memory available to the iterative method. The memory used are limited by the app but experience have shown me that it is enough for reasonable grained results

Help

Help - Don't read this. You'll get confused
About - Beyond the scope of this document

At any stage of fractal display, you may resize the window which will result in the fractal being regenerated to fill up as much as possible of the window without aborting aspect ratio.

Installation

For the following instructions to work, the user this is done with should have access to developement tools on target host and write access to installation directory

Unpack distribution
In distribution root directory do

./configure
make
make install

In you have any problems and/or patch to installation process, please let me know.

You should have received some sample .tur files in the distribution. Try them out.

Bugs

When starting up, it might happen that the splash screen is not displayed correctly
Linear fractals take a very long time to reach maximum iteration level which makes it look as if the system hung

Changes

23 September 1997 - Version 0.1 released

Acknowledgements

The idea stemmed from an application called Fractree running on the platform of the enemy which I used some 4 years ago and which I enjoyed playing with a lot ( i mean the app not the OS ;-). It was written by Michael Schernau. I include some fractals from his original implementation.
The guys at Troll Tech which created such a nice application framework which makes it the easiest i've ever experienced to write GUI's
The guys at the core of KDE which spawned such a great project for Linux
The Linux team for relieving me of the agony ( and i'm serious ) of working with a lesser able though better known OS and providing one in which i feal generally protected...

Pheewww ...

Future

In future, this app might inspire me to implement a seperate Logo programming environment for KDE
I also have in mind adding color variation support to the turtle command set
I want to write a screensaver companion for KDE based on the turtle and fractal sets as encountered in this app and after color variation was built in

Copyright

I must admit, i don't understand neither copyright statements nor their laws. I include a copy of the GNU General Public License just to have something to put in this section, so your bound to it.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA

If needed, contact me at tiaan@netsys.co.za