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--- pix_strange_attractor [2007-06-20 18:19] – pix
+++ pix_strange_attractor [2007-06-21 08:07] – nik
@@ Line 106: / Line 106: @@
-as an aside i realised that different starting points is just the same as choosing different coefficients, since the effect of choosing a different starting point could also be achieved by shifting the graph by a constant offset, which can be achieved by changing the coefficients.
+as an aside i realised that different starting points is just the same as choosing different coefficients, since the effect of choosing a different starting point could also be achieved by shifting the graph by a constant offset, which can be achieved by changing the coefficients. //wow, this is super-wrong. although this assumption kind of holds with a normal polynomial, if you start iterating, it all falls down.//
 ==== 17 Dec 2006 ====
@@ Line 245: / Line 244: @@
 it would be also interesting to have an automatic parameter fudger (like my applet) but with more parameters controlling the automatic search. for example, hill climbing to maximise some metric. in the sprott book, there is some data correlating how highly people rated a given attractor and cross referenced to the values of the two metrics. there was an obvious maximum for particular values of both. it would be interesting to hunt towards attractors that had these 'optimal' properties.)
 ==== 20 Jun 2007 ====
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 it would be really interesting to be able to click around on this image and see the attractor that each point represents. i' not sure yet if that will make it into the research or if it will be a future direction.
+=== Yet another animation ===
+Oh, and there is this neat new animation. First some ramblings. I was showing the parameter plots above to Tim Boykett, and he pointed out an important assumption that I was making. The plots are specifically plotting the presence of attractors that just happen to have 0,0,0 in their basin of attraction (because the function doing the escape-plot always uses 0,0,0 as the starting point). To investigate how important this assumption was, I made an animation of parameter plots for changing initial values. The base attractor is the one used in all of the images called "highf" above. At the start of the animation, the initial value used for the parameter plots is -1,0,0, and by the end it is 1,0,0. In the middle of the animation, you should see a frame that looks like highf-c00-01-512esc20.png above (only with the black part filled in white, and rotated 90 degrees counter-clockwise - the renderer has changed a bit) when the initial value hits 0,0,0.
+[[http://lib.fo.am/_media/movingbasin.gif|{{movingbasin.gif?64x64|click for full size}}]]
+{{movingbasin.gif?64x64|click for full size}}
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