This Applet allows you to create self-similar fractals and edit them in real time. There is a brief description
Brief Applet Description.
- Self-similar fractal is generated by a system of contractive similarities.
The Applet uses special color for representing each contractive map.
- You can find gray segment in the center of applet.
The applet applies each map to this segment and gets a
shorter segment and draws it with the color corresponding to this map.
The idea is that to each fractal map the unique, except for reflection and reverse, color segment is related.
Moving the segments you can modify the maps.
To change the direction and turn on/off map reflection there are a special button and a switch.
- The applet stops building the fractal, if at least one of the maps is no more contractive, i.e. if corresponding segment became longer than initial gray segment.
- The end points of the segments can be moved with the mouse. Close points glue and move together.
- The glued point can be torn off when pulled with SHIFT pressed or with right mouse key. To know exactly a point of which segment you are going to tear off first select the segment by clicking on itself or by clicking several times on its end (the clicks will sequentially select all the segments for which this is an end point).
- To change the map reflection and reverse fist select corresponding segment.
- Here is one of the algorithms for building a fractal using the segments. A professional eye will notice that the fractal images built this way are similar to L-System fractals.
The algorithm draws images of the gray segment according to various superpositions with length n of the initial maps.
The length of the used superpositions n is conventionally called the number of iterations.
Description of buttons, switches and list boxes.
- The first list box contains classical samples of self-similar sets (the Koch and Levy curves, dragon broken line, Sierpinsky triangle).
The value «User...» means that the fractal has been modified and is no classical any more.
- List of numbers for choosing the number of iterations which is used in building the set by lines.
- If you cannot see the fractal behind the initial color segments hide them using option Hide first
- The switch By points sets the type of drawing algorithm - by segments or by points.
- The Reverse map button reverses current map by 180 degrees.
- The switch Reflection defines if current map reflects about a line.
The Koch curve is generated by maps with reflection.
- The Add map button adds a map.
- The Remove map button removes a map. A map cannot be removed if there are only two maps left.