[chaoscope] Re: Beta .2 again

  • From: Chaoscope <chaoscope@xxxxxxxxxxxxxx>
  • To: chaoscope@xxxxxxxxxxxxx
  • Date: Sun, 18 Apr 2004 14:41:38 +0100

Attached is a screencap of an error I just got (it's a little bigger than ususal 69KB, but it shows the info in the palettes as well) You can recreate this error with this screencap. (Sidenote: the Tab order in the floating palettes is very strange. It also does not visibly show you focus unless you're in the Type or Render box.)

69Kb?! You're fired!

It's not an error. I will change the icon to an exclamation mark, the white cross icon is reserved to critical errors.

Sometimes the orbit escapes the attractor after a few thousands iterations. It's either due to the attractor being weak and/or accumulated floating point calculation imprecision.

It happens as well on version 0.1, however the rendering just stops and you don't get a dialog box.

What may also happen is the attractor will lose its "strangeness" and switch to a different phase, to become a one-dimensional (a circle) or zero-dimensional attractor (one or several points). This can't be detected during rendering because the fractal dimension of the attractor is only calculated during search. It's up to you to keep an eye on the view, or the number of iterations per second, which goes up because the processor cache hits ratio gets higher.

side-note : to make a smaller screen capture, restore the MDI window, move the palettes within the MDI window and press Alt+Print Screen, which copies the active window instead of the whole screen. Obviously, it's got to be done before a modal dialog box appears.

Side-side note: I am no mathematician, so maybe there's a good answer to this but, with the sliders in the Attractor palette you can easily go outside the range of acceptable values manually. With each attractor type, is there a well defined min and max for each param? If so, how much of a pain would it be to limit the sliders to the values? So if I pick Lorenz-84, paramA's slider will go from -1 on the low end to +1 on the high end (I'm just making up numbers for the argument!) That way if I am manually adjusting the attractor I won't be running into values that won't produce a result. (I am a big advocate of manual control. The search option is nice for a starting point, but I'd rather build these forms by more manual control.)

The best attractors are found manually, so you are right on that.

All attractors parameters do have a well defined limit, which is also the range of the sliders. They have been fixed empirically, as a boundary to the parameter space where most strange attractors are concentrated.

If you think of the three parameters of the Polynomial A equation as the coordinate of a point in a 3D space, you can imagine a set of points in this space for which parameters will yield a strange attractor. This is similar to how a Mandelbrot set is calculated : the parameters of the equation are the real and imaginary parts of Z, and the points within the set are those for which parameters yield an attractor, where the orbit doesn't escape or bailout.
As you know, the boundary of the Mandelbrot set is not only extremely complex, it is also fractal, and although I believe the Polynomial A set isn't equivalent in complexity nor is fractal, it isn't just a spheroid.

Keeping the Polynomial A as an example, the minimum and maximum values of each parameter are the opposite faces of a cube which is its search domain. Each parameter is a line parallel to each axis going across the cube, so the three lines intersect at the same point, within the cube. Going along one of the lines, you can see what parts of the line are inside the attractor set, i.e. what values of the equivalent parameter will yield an attractor. These values won't be contiguous.
Of course, when you modify a value, or move the intersection point along one of the lines, the two other will move as well, thus going through a different part of the attractor set.

Therefore it's not easy to define a search domain, or the parameters range, without limiting too much the set of possible attractors. But a larger search domain makes manual search a long-winded process.

I've been thinking about rendering these sets : the user would have to select three or more parameters and define their corresponding plane (ex. P0 -> X, P1 -> Y, P2 -> Z, etc.). Imagine doing it with all the parameters of the Polynomial C, in an 18 dimensions space!

Nicolas Desprez
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