Fractal visionaries:

For the month of August I've decided to devote less energy to the technical side of fractals and more to the artistic side.  True, the four-dimensional julibrot figure with its odd slices is fascinating, but an infinity of fractals is waiting to be discovered in the good old Mandelbrot and Newton's worlgs.

I'm certainly not going to abandon my exploration of the julibrot.  Every time I examine it I find something new and interesting.  I'm rather going to try to divide my time evenly between all the various classes of fractals.

Today's fractal is a good start.  The formula is one of my test formulas that I wrote a while back and then forgot.  But it's really quite an interesting formula, with its tiny portion of opposite signed imaginary powers cancelling out the negative X-axis discontinuity.

I named the picture "Cogwheel" because it reminds me of some fantastic train of gears and gear belts.  Look close and you'll find the classic Z^2 Mandelbrot figure hiding behind the scene.

The finished image has been posted to alt.binaries.pictures.fractals and alt.fractals.pictures.  For tomorrow, the sky is the limit.  I'm going bring up a few more of those old test formulas and see what I can find.

And as I promised in yesterday's letter, I've decided on descriptive names for the four odd slices of the julibrot.  Here they are: they describe the appearance of the slices in question through the julibrot origin.

XY = Mandelbrot planes
ZW = Julia planes
XZ = Parabolic planes
XW = Elliptic planes
YZ = Oblate planes
YW = Rectangular planes

When I return to the julibrot figure, I'll be using those names to describe the planes I'm referring to.  That way we'll avoid confusion.

Jim Muth
jamth@mindspring.com


START 19.6 FILE=============================================

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frm:Mytest10  {; Jim Muth
z=c=pixel:
z=z^p1+p2*((z^p3)^(-p3))+c,
|z|<=100 }

END 19.6 FILE===============================================