; Date: Mon, 08 Jun 2009 17:00:16 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 09-06-09 (Seahorse Valley-09 [6]) ; Id: <1.5.4.16.20090608170136.2bbfef06@pop.mindspring.com> ; --------- ; ; FOTD -- June 09, 2009 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; While viewing today's image, which is the last time we'll see ; this particular Seahorse Valley minibrot, I started wondering ; exactly what a minibrot is. In the Mandelbrot set, minibrots ; appear as miniature Mandelbrot sets. But at the same time mini- ; brots extend beyond the Mandelbrot set in 2 perpendicular Julia ; directions, making it more appropriate when discussing minibrot ; rotation to consider minibrots as four-dimensional 'minibrot ; complexes'. ; ; The elements in these complexes are very large in the Z-plane ; directions and small in the C-plane directions. The complexes ; are open inside and extend throughout the Julibrot figure, ; appearing here and there until they are ultimately completely ; cut off by lower-iteration stuff. The great difference in the ; C and Z dimensions of the minibrot complexes also explains the ; extreme stretching that so often appears in the odd-plane ; directions. ; ; Today's image is another view of the past two days' minibrot ; complex, this time sliced in a direction rotated about halfway ; between the Oblate and Rectangular directions. Conveniently, it ; has X-axis symmetry, which not only gives a more pleasing appear- ; ance, but also cuts the calculation time in half. I had to ; stretch the image quite a bit in the horizontal direction to ; make it clear. ; ; Unfortunately, I could not rate the image at a 9, as Paul ; wondered, since this is the third consecutive trip to the same ; minibrot complex. But the rating of a 6 is still a bit above ; average and makes the 5 minutes required to run the parameter ; file just barely worth the effort. ; ; perhaps the best way to view the image is to surf out to the ; FOTD web site at ; ; ; ; but try not to fall into the 4th dimension on the way. If you ; got turned around there, you would come back as anti-matter and ; destroy half the continent when you self-annihilate. ; ; The fractal cats enjoyed the typical early summer weather that ; prevailed here at Fractal Central on Monday. The temperature ; of 86F 30C and the humidity did not bother them at all, but I ; decided it was time to get the energy-saving fan out of the ; closet and stir up a breeze or two. ; ; The next FOTD will be posted in 24 hours. It will not be just ; another view of the same minibrot. Until then, take care, and ; would it be possible for a universe to exist with no conscious ; observers to observe it? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Seahorse_Valley-09 { ; time=0:05:12.20-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t periodicity=10 center-mag=0/0/108000/50000000/0 params=42.6/90/0/90/-0.7499841692570846/0.01444653\ 20644315/0/0/2/0 float=y maxiter=16000 inside=0 logmap=2000 symmetry=xaxis mathtolerance=0.05/1 colors=000zzzQYxTWwWUvZSuaQudOtgMsjKrmIqmGqkHmiHjg\ HgeIccI`cIYcJUcJRdJOeJLfLKgNJhPIiQHjSGkUFmVEnXDoZC\ p_BqaArc9sd9tc8ub7va6w`5x_4yZ3zY3vY8sYDoYIlYNhYSeY\ XaYaZYfVYkSYpOYuLYzOXxQXvSWuVWsXVrZVpaUocUmeUlT`bG\ gT4mJ8rLBvMEzNHzPKzQNvRQrTUmUXjV_iXbiYeiZhh`khanhb\ dg`VgZLgXBgVwpGumFsjEqhEoeDmbCk`CiYBgWBeTAcQ9aO9_L\ 8ZJ8ZO7ZT7ZX7Za7Zf7Zj7YiCXhGWgLWfPVeUUdYUdaYbbaabe\ `ch_ceYZcWU`UQZTLWRGUPCRN7PM3CEM07d66aC6ZH6XN5US5R\ Y5Pb4Mh4Jm4Hi5Ee6Ba69Y76U83Q81P95OA9NBDMCHLDKKEOKF\ SJGWIH_HIbGJfFKjELnEMqGQmHUiIXfJ`bKdZLgWMkSNoOmr0P\ vzQyzRuzRrzRozRkzShzSeLSaMSZNTWOTSPTPQTMRTJSRHQPGP\ NFNLDMJCKHBJF9HD8GB7E96DDBCGFBKJANO9QS8UW7X`6`d5ch\ 4fl3gg5hb6iY7jT8kP9lKAmFBnACo5Dz00z00z00z00z50zA0z\ F0zK0zP0zS0zV0zY0z`0zc0zf0zg0zi0zk0zm0zo0zq0zs0zu0\ zv0zw0zx0zy0zz0zz0zz0zz0zz0zzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint