If finding a decomposition is difficult, here are two approaches for building intuition. The first uses paper and scissors, the second uses the web and a graphics program.
First approach:
| * Trace the main features of the fractal and cut out smaller copies of the tracing. |
| * To allow for reflections, flip the small copies and on the back trace over the lines on the front. |
| * Place the small copies, perhaps rotating or reflecting them, to make a copy of the original fractal. |
Second approach:
| * Bring up the homework web page on your computer. |
| * Place the mouse arrow over the fractal image whose IFS rules you wish to find, hold down the mouse button until the menu pops up, and select "copy this image." |
| * Now open your graphics program and paste the image. This is the target image. |
| * Paste another copy and use the graphics functions - scale, rotate, reflect - to cover one of the pieces of the target. You must be careful about the placement of the pieces under rotation and reflection, but the animations mentioned above seem to be good preparation for this. |
| * Continue until all the pieces of the target are covered. |
Test the transformations by running the IFS program.
Return to the Inverse Problem.