Title: why dont use Vector Cross Product as Multiplikation ?
Post by: cKleinhuis on November 16, 2010, 02:33:31 PM
i just read about algebras, and found that vektor cross product can be used to define the multiplication, perhaps it
could lead to nice results, although definitive no mandelbrot shapes, but worth a try ;)
could lead to nice results, although definitive no mandelbrot shapes, but worth a try ;)
Title: Re: why dont use Vector Cross Product as Multiplikation ?
Post by: hobold on November 16, 2010, 06:02:59 PM
The vector cross product of a vector X with itself is always the zero vector. In other words, the cross product cannot directly be used for the squaring of z^2 + c. There could well be other uses for the cross product in other formulas, though.
Title: Re: why dont use Vector Cross Product as Multiplikation ?
Post by: M Benesi on November 17, 2010, 01:17:51 AM
I've used dot product to find angles between a vector and an axis. The same can be done with the cross product. Determining what to do with those angles is the issue :D.....
Title: Re: why dont use Vector Cross Product as Multiplikation ?
Post by: cKleinhuis on November 17, 2010, 01:58:46 AM
The vector cross product of a vector X with itself is always the zero vector. In other words, the cross product cannot directly be used for the squaring of z^2 + c. There could well be other uses for the cross product in other formulas, though.
i see, that makes no sense :(
Title: Re: why dont use Vector Cross Product as Multiplikation ?
Post by: fractower on November 17, 2010, 05:02:20 AM
Cross products can be very useful for producing rotations. Specifically if you have two vectors 
and 
then the cross product will be a vector 
which is perpendicular and . The magnitude of will be proportional to 
. Where 
is the angle between and . The part is mostly a pain since you really want to normalize . Give a normalize vector 
one can easily produce a rotation matrix (Google has a good description). I keep a set of tinker toys handy for when I need to do vector operations.
I have attached a pointer to an image and a write up of an algorithm I have been playing with that makes a lot of use of cross products..
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=3286 (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=3286)
http://www.fractalforums.com/new-theories-and-research/tinker-towers/msg21004/#msg21004 (http://www.fractalforums.com/new-theories-and-research/tinker-towers/msg21004/#msg21004)
I have tried throwing random vector operations together. For the most part the results are boring, If I come up with something interesting however, I am perfectly willing to say "I meant to do that."
I have attached a pointer to an image and a write up of an algorithm I have been playing with that makes a lot of use of cross products..
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=3286 (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=3286)
http://www.fractalforums.com/new-theories-and-research/tinker-towers/msg21004/#msg21004 (http://www.fractalforums.com/new-theories-and-research/tinker-towers/msg21004/#msg21004)
I have tried throwing random vector operations together. For the most part the results are boring, If I come up with something interesting however, I am perfectly willing to say "I meant to do that."