FOTD -- October 27, 2007 (Rating 8.5) Fractal visionaries and enthusiasts: Let's have a little philosophical Halloween diversion before we get to the fractal discussion. Halloween is but four days away and everyone is thinking of ghostly things. In keeping with the spirit of the season, I was stopped on the street this morning by a reporter from the local newspaper and asked if I believe in ghosts. Apparently they were taking a poll of the local population. Since I had no time to spare, my answer was simply 'no'. But the facts are not so simple. Ghosts do exist! One thing for certain is that people do see ghosts. Legends of people being visited by ghosts exist in every culture. The question should have been, 'what do you think ghosts are?' Then I could have given the two most obvious answers: 1 -- A ghost is the surviving spirit of a dead person. 2 -- A ghost is an internally-generated mental image projected outward into the real world. Neither answer is totally satisfactory, since both answers raise more questions than they answer. The first answer raises the question of the existence and nature of surviving spirits, while the second answer questions the nature of both mental images and the external world. And the claim that a ghost is a mental image induced by the presence of a surviving spirit brings everything into question. IMO, it all comes down to the age-old problem about the nature of reality. If we could ever answer this question, (which I doubt), most of the other haunting questions would likely be answered at the same time. And speaking of ghosts, I was really spooked by today's image, which lies in the parent fractal that is created when 0.8 negative parts of Z^(-8.8) are combined with 5 negative parts of Z^(-1.8) and (1/C) is added. This parent consists of two large circular bays surrounded by many smaller irregular bays and minibrots. Today's scene is located on the shoreline of one of the large circular bays, in an area that at first appears to be totally non-critical, and where a pure minibrot would be the last thing expected. But not being put off by the apparently impossible, I checked the hopeless area anyway, and much to my surprise, I found a well-hidden minibrot. This minibrot lies nearly invisible at the center of today's image. The image was rendered in an unusual manner, with both the inside and outside parts set to 'fmod'. To see which parts are 'inside' and 'outside', reset the inside option to 'numb' and the outside option to 'iter'. The name of today's image, "Unexpectedly There", is a simple statement about the scene. The rating of 8-1/2 rewards me 1/2 point for the extra effort I put into smoothing the colors. The calculation time of 10-1/3 minutes may be cut by a minute or two by setting the passes to 'g'. But doing this misses some of the finer parts of the spirals. The all-around best way to see the image is to view it in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds, steady rain, and chilly temperatures made the Friday weather unpleasant here at Fractal Central. The fractal cats seemed to agree, for they spent a good part of the day snuggled in the warmest places they could find. My day was busy enough that I had little chance to complain about the inclement weather. The next FOTD will be posted in 24 hours. Until then, take care, and the next time you see a ghost, say to it: 'what are you and what do you want?' Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Unexpectedly_There { ; time=0:10:19.52-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=+0.723105839047/-0.510872744279/4126147\ /1/-62.5/8.37e-006 params=-0.8/-8.8/-5/-1.8/0/0/0/0 float=y maxiter=5000 inside=fmod proximity=0.8 outside=fmod periodicity=10 colors=000cnjdnifnggnfinejndlncmnbonaqsdpn`piXodTo\ _PnVLnQHmLDmG9mB5iC9fCCcCF_CJXCMUCPQCTNCWKCZHCaGF`\ FI`EK`DN_DP_CS_BU_AXZ9_Z9aZ8dY7fY6iY6kY8oY9sYBy`Av\ YAtWArUApRAnPAlNAjKAhIAfGBdHBcICbICaJD`KD_KEZLEXMF\ WMFVNGUNGTOHSPHRPHQQIORINRJMSJLTKKTKJULIULGVMFWMEW\ MFXMGYMHYMIZMJZMK_ML`MMaMNbMOcMPdMQeKReJSeITeGUfFV\ gDWhCXiAYj9Zj9Zj8Zo8_o8_o8`o8ar8bs7cn7dp7er7du7ew7\ gz7gw7ht7jq7jn7ll7ni7nf5odApcFpaKq_PrYUsXZsWcrWhrV\ kqVnqVqpUtpUuoUvoTwoTwnSwmSwlSwkRwjRwiRvhQwgQwfPve\ PtdPrcOqbOpaOn`Nl_NkZMjYMhXMgWLeVLdULbTM`SN_SOYRPX\ RPVQQTPRSOSQNSPMROLQOKPOJOOINOHMNGLMFKLEKKDKJCKHBK\ GAKF9KF8KG7KH6KH5KI4KJ3KK2KL1KK0KK0KK0KK0KK0KJ0MJ0\ OJ0QJ0SJ0UJ0WL0YN0ZO0ZQ0_R0aT1cU2eW2iX3kZ3m_3oa3qb\ 3sd3ue3wg3zi2yh3xg4wf5ud6sc7qb8oa9m_AkZBiYCgWDeVEc\ UFaTG_RHYQHXPHWNHVMHULHTKHSIHQHIOGKMFLKKNGOPDSRHWT\ L_VPcWTcXXcY`cZdc_hc`gcag } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================