Lesson 1     Lesson 2     Lesson 3     Lesson 4     Lesson 5     Lesson 6     Additional Information     Glossary of Terms     Links & Resources Lesson 1 – Page 4:Iterations     The complexity of the Mandelbrot structure is related to the number of times we allow the formula to iterate.     Highlight, copy, and paste this parameter set (everything in purple) into an open UF window: oneIteration { fractal:   title="one iteration" width=400 height=400 layers=2 resolution=200   credits="Janet Parke;7/30/2005" layer:   method=multipass caption="Mandelbrot outline" opacity=100 visible=no   transparent=yes mapping:   center=-0.692/0 magn=1.3586957 formula:   maxiter=100 percheck=off filename="Standard.ufm" entry="Mandelbrot"   p_start=0/0 p_power=2/0 p_bailout=4 inside:   transfer=none solid=25210 outside:   transfer=linear solid=4286722382 filename="lkm.ucl" entry="basic"   p_colorby=iteration gradient:   linked=yes smooth=yes index=0 color=0 index=200 color=16777215 opacity:   smooth=yes index=0 opacity=0 index=200 opacity=255 layer:   method=multipass caption="Iterations" opacity=100 mapping:   center=-0.692/0 magn=1.3586957 formula:   maxiter=1 percheck=off filename="Standard.ufm" entry="Mandelbrot"   p_start=0/0 p_power=2/0 p_bailout=4 inside:   transfer=none solid=4278215290 outside:   transfer=linear solid=4294901760 filename="lkm.ucl" entry="basic"   p_colorby=iteration gradient:   linked=yes smooth=yes index=0 color=0 index=200 color=0 opacity:   smooth=yes index=0 opacity=255 index=200 opacity=255 }     There isn't much happening in this image yet because we have limited the calculation formula on the bottom layer to just one iteration. This results in most points (except a few on the left side of the image) still being "inside" points after one iteration. Make sure that the bottom (Iterations) layer is active and then change the Maximum Iterations on the Formula tab to 2. Continue increasing the iterations by increments of 1 and note how the outline of the turquoise shape becomes wavier.     When you reach a Maximum Iterations value of 5, enable the top (Mandelbrot outline) layer. This will overlay a more detailed outline of the Mandelbrot shape over your iterations layer. As you continue to increase the Maximum Iterations on the bottom layer in small increments, you will see how the outline of that layer begins to more closely resemble the white outline in the top layer. By 20 iterations, the turquoise in the bottom layer begins to nearly match the white outline in the top layer.     At this point, disable the top layer again so you only see the turquoise and black bottom layer. Now change the Maximum Iterations from 20 to 100 and watch how the pinched areas where each disk joins the main cardioid close and sharpen. You can toggle between Undo (Ctrl+Z) and Redo (Ctrl+Y) to quickly see the differences.     For initial exploration, 100 iterations is sufficient. We'll talk about when and why to increase them later. Back – Lesson 1 – Page 5 Copyright © 2005-2011 Janet Parke