; Date: Mon, 29 Jun 2009 17:51:18 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 30-06-09 (Seahorse Valley-30 [8]) ; Id: <1.5.4.16.20090629175256.2b8f62d8@pop.mindspring.com> ; --------- ; ; FOTD -- June 30, 2009 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; Today's image is a puzzle. Everyone knows that Mandelbrot-type ; minibrots are impossible in Julia sets, so how do we explain the ; obvious midget M-set in today's image, the parent of which is a ; Julia set. To see this Julia set, reduce the magnitude to 0.5 ; and recalculate the image. The Seahorse-Valley Julia set that ; soon fills the screen is obvious. ; ; Well, two things need to be explained. To begin, the minibrot ; is somewhat warped. Its two period-3 buds as well as its main ; stem are missing. And in addition, the parent Julia set is not ; quite a Julia set. It is double-rotated 1/1000 of one degree ; from the true Julia orientation. This rotation is extremely ; small -- the width of one centimeter as seen from a distance of ; over 1/2 kilometer -- but it is enough to reveal the Mandelbrot ; shape of the minibrot. To see the minibrot magically turn into ; the Julia set of the center of the main Mandelbrot bay, change ; real(p1) and real(p2) to 90. Yes, 1/1000 of one degree can make ; this much of a difference. ; ; Other things of interest are the four partially-filled peanut ; holes and the breakdown of the 2,4,8... series of elements ; surrounding the minibrot. This breakdown is no surprise, since ; it often appears in warped minibrots such as the minibrot in ; today's image. The unusual texture of the image was achieved by ; rendering it with the outside set to 'summ'. ; ; I rated the image at an 8. I think it has enough interest to ; earn such a rating. The calculation time of just over 9 minutes ; is rather slow, but nothing to get excited about, especially ; since the image may be viewed on the FOTD web site without the ; need to calculate it. The web site may be accessed at: ; ; ; ; Picture perfect weather prevailed here at Fractal Central on ; Monday -- at least the fractal cats thought so. They thoroughly ; enjoyed the blue skies, puffy white clouds, low humidity and ; temperature of 84F 29C. ; ; >From indoors I half enjoyed the outside conditions. Meanwhile, ; FL, having asked a question on Sunday that I had no immediate ; answer for, enjoyed an afternoon in her garden, keeping a sharp ; lookout for japanese beetles in the roses. ; ; The next FOTD, the first of a new month, will be posted in 24 ; hours. I wonder what the new theme, if any, will be. Until ; then, take care, and the pleasantly cool summer we're having ; this year should quiet those greenie fanatics clamoring about ; the imaginary perils of equally imaginary man-made global ; warming . . . at least until it gets hot again. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Seahorse_Valley-30 { ; time=0:09:05.19-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 center-mag=-0.000394521/0.010564/31.23732/1/72.5/0 params=89.999/0/89.999/0/-0.7500830511589915/0.007\ 7264749796986/0/0/2/0 float=y maxiter=15000 inside=0 outside=summ periodicity=10 colors=000mO2zP5mP6la8mPAzPCmPDzPEmOKaMNYLSVKWSJ`P\ IfMHkKGpJLlJQiJVgJZcJcaJh`KnXKsVKxTQwXUv`Zvbctfhsi\ lslprpsssxsutprqlonhmkfjhbgeZebXb_T`YQYUNWRKTOGRME\ QPHTTKWWMY_Q`bSbfVeiYhm`kqcntfpxiszkuznxzluvksrjqn\ hpigmgflbdiYbhVagYihbskdzlczhczebzbazZ`zW`zSZzP_zL\ YzIYzESs8Mk2Gc0JgBLkOMn`OzzPezPzzPezQezzzzQzzQezRe\ zzvzRezRtSSuzSezSezSezzzzTxJzyIzzHTzGTzESzDTzDRzCQ\ zCOzBOzBNzALz9Lz8Kz8Jz7Iz7Hy6Fy6Fy6It8KpAMkCOgFQbH\ SYJTVLWRNYNP_KRXMQWNQTPPSQPQROQSOOVNNWNLYMK_MIaLHb\ LEeJDfKEeLGeMHeNIcOJcPKcQLbRObTPbUQaVRaWSaXT`YU`ZW\ `_X_`Y`aZ`b`````_b`Yc`WfaTg`RcfS_kUWqVTvVStUSsUSrT\ SqTSpSSpSSnSSmSRlQRlQRkPRiPRhORgORfOQeMQcMQbLQbLQa\ KQ`KQ_KQYJQXIPWHQVHPTGPTGPSGPRFPQFPPEPOEPNCPMCPLCP\ KBPJBPIAPHAPG9PF9PE9PD8PC8PC7zC8PA5P85m97P64P54m65\ P33bHHzHHaGG`EEmGG_EE_DDmEEmDDmDDzzDmCCzCCzzCmBBzB\ BzzAmAAzAAm88zz1zY0zQ0zz1 } 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