## [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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