[chaoscope] Re: Would like to know more about color gradiants
- From: Chaoscope <chaoscope@xxxxxxxxxxxxxx>
- To: chaoscope@xxxxxxxxxxxxx
- Date: Fri, 16 Jun 2006 23:34:01 +0100
Hello Christian,
I really like Chaoscope and I love it to play with this great tool.
But there is one thing I would like to have more information about. I
mean the two different color gradiants (speed and angle).
Is there a chance to get more information about how they work?
There is only one sentence about them within the manual and I've not
understand it.
Some more details would be great.
I'd love to give you as much detail as I can about how the colors are
assigned to each point of an attractor but I'd be worried about boring
the hell out of the subscribers. So I will be short.
Every attractor is made of points, coordinates in a three dimensional
space. The coordinates are the result of an equation and one point is
added every time the equation is calculated. The points appear in a
random order on the surface of the attractor. Each time a point is
added, Chaoscope measures the distance between the new point and the
previous point, the distance is normalised (the minimal distance becomes
0 and the maximal distance becomes 1) and is mapped to the speed gradient.
The angle requires one more point. Say for instance we call the last
three points A, B and C. Chaoscope calculates the dot product between
the vector BA and and BC, normalises the result, maps it to the angle
gradient and gives that color to B. The dot product between two vectors
is equivalent to the cosinus of the angle they form: -1 when they point
to opposite directions, 0 when they form a square angle and 1 when
they're parallel.
I hope I've satisfied your curiosity, let's carry on this discussion
outside the mailing-list if you require more information.
Kind regards,
Nicolas Desprez
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