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 float=y passes=1 inside=0
  center-mag=-0.000394521/0.010564/31.23732/1/72.5/0
  params=89.999/0/89.999/0/-0.7500830511589915/0.0077\
  264749796986/0/0/2/0 maxiter=15000 periodicity=10
  outside=summ
  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=========================================