News: Did you know ? you can use LaTex inside Postings on fractalforums.com!

## The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!

elephant
Previous Image | Next Image
Description: next attempt, like in wonderful mandelbulb, angles are measured, theta around the equator, phi through the poles. phi is measured in multiples(or parts) of pi, the respective value afterwards squared. Theta is doubled. z1 is determined as a point in a coordinate system, theta along the x-axis, phi along y-axis. the distance from zero on the z-axis, in logarithmic scale. the unit sphere will be mapped onto a rectanglenear the origin. the mandelbulb algo is done by choosing a point on the equator, from this point doubling the distance to any point z1, so we will reach z2. Taking the point on the line, which is representing the north-pole, we will get algorithms (similar to the squaring of quaternions,), they are implemented in T. Gintzīs Quasz as "gedatou" and "ventri".(Squaring quaternions is done by doubling phi, measured from the pole, theta remaining unchanged. We can imagine a rubber-ribbon around the equator. Measuring phi from it, we get mandelbulb("rings of fire" in Quasz-but only for power 2), sliding the ribbon to the north-pole, the mandelbulb-algo will change to "gedatou"(if the ribbon is shrinked to one point on the line, representing the pole, if the ribbon is extended along this pole-line, it will change to the squaring of quaternions, so we may see the connection between squaring of quaternions and hypercomplex numbers). Using this coordinate system, we get a certain freedom to develop new algorithms, even sometimes preserving the mandelbrot set in one plane. In this picture still same angles phi are mapped to points with same angles phi2, maybe we could change this to get more harmonic structures in all(?) directions?
Stats:
Total Favorities: 0 View Who Favorited
Filesize: 89.19kB
Height: 675 Width: 1264
Keywords: mandelbrot set threedimensional 3d   mandelbulb gedatou ventri rings of fire
Posted by: vector January 03, 2010, 08:31:59 PM

Rating: by 3 members.