; Date: Thu, 03 Jun 2010 22:35:41 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 04-06-10 (Marshmallow Design [9.5]) ; Id: <1.5.4.16.20100603223657.2b97f74e@pop.mindspring.com> ; --------- ; ; FOTD -- June 04, 2010 (Rating 9.5) ; ; Fractal visionaries and enthusiasts: ; ; Today's image could almost be a photograph of a 3-D scene. ; Actually, there is nothing 3-D at all about it. It is totally ; 2-D, a flat scene in a fragmented elephant in the rudimentary ; East Valley of the parent fractal that results when the expres- ; sion Z^(1.5)+C is iterated 12 levels up the logarithmic ladder ; with the 'round' function applied. ; ; The 3-D effect is a combination of the coloring and the basic ; underlying iteration bands. But it is an illusion. The wrong ; colors will totally destroy the 3-D effect. ; ; Actually, the visual 3-D view we have of the so-called outer ; 'real' world is also an illusion. The images on our retinas are ; totally 2-D. The third dimension appears in our awareness when ; our mind (or brain if you're a materialist) compares and com- ; bines the two slightly different images sent to it by our two ; eyes. ; ; Does this mean that the 3-D solidity of the outer world is also ; an illusion? I often wonder. True, the outer world obeys the ; mathematical laws of 3-D space, but we ourselves invented mathe- ; matics and tweaked its rules so that it works correctly when we ; apply it to the world we assume exists around us. ; ; We can prove that the universe is three-dimensional by observing ; the orbits of the planets. It can be demonstrated mathemati- ; cally that stable planetary orbits are possible only in spaces ; of two or three dimensions. Of course, if we lived in a world ; of four spatial dimensions, we would have developed a math that ; demonstrates that stable orbits are possible also in spaces of ; four dimensions. ; ; Now back to the image. ; ; I named today's image "Marshmallow Design". I must have had a ; fleeting impression of roasting marshmallows while trying to ; think of a name. The rating of a 9.5 is exceptionally high, and ; includes a generous self-reward for the coloring, but I think ; the image is worth it. ; ; The calculation time of 1-2/3 minutes will be no problem for ; those who cook their own fractals. Those who prefer their ; fractals pre-cooked and canned may view the finished image on ; the FOTD web site at: ; ; ; ; Typical summer weather made Thursday a typical partly cloudy ; summer day here at Fractal Central. The fractal cats thought ; the temperature of 88F 31C was a bit warm, but with the cool ; tile floor to stretch out on, they did not complain too much. ; My day was about average. ; ; The next FOTD will be posted in 24 hours. Until then, take ; care, and the greedy big-oil guys are getting worried. So keep ; pumping and reassure them that we still depend on them. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Marshmallow_Design { ; time=0:01:40.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=round logmap=270 center-mag=+0.159907326462106/-0.00233287824442478\ /1.136758e+013/1/-27.9/0 params=1.5/0/12/0 float=y maxiter=1500 inside=0 mathtolerance=0.05/1 colors=0004Ab17c48e79gAAiDBkGCmICoMEmQGiUHdYJ`aLWe\ MSiONmPJnNIoMHoLGpKGpJFqIEqHDrGDsECsDBtCAtBAuA9u98\ v87v77vEBzwmyykxxiwwgvvettcrraoo_llYiiWffVccT__RWX\ PSTOOPMLMKIJIGHGEFECDCABA8986764542321200100000000\ 00000000000AAAKKKUU_ZZYS`VLaTEjRJhSOfSTdSXbSa`SfZS\ kXSoWSn_QzzczxczuzvszrqmmocdmUXdSPWWGSU8OS0MQ0KO0I\ M0GKm`5gd9ciEceEcaBhY9mU7rQ5sO7tL6sS5rZ4qe3pl2os1n\ y1mn5ac9VUDNJHG9KUHLgPMtWMneRhoVbyZRjBPhANf9Le9Jc8\ Hb8F`7E_7FZEGYKHXQIWWJVbKUhLTnMStV_lcgdloXuwQorSjm\ TehV`cWWZXRUZMP_HL`KzzzzzEzzmzzEzzmzzDfRDcPIgPNjPS\ mPXpPasPevPhqSjlUlgWnbYpY_rUalTXfSTaROWQKQPGLOBFN7\ AM3HK5NJ6TI7ZH8dG9fEDgDHhCLjBPkATl9XjIRhRMf_HdhCcp\ 7UiHKbRBW`FX_IY_LY_OZ_R__U__MdRFiz8nzArzAszAtzFuzH\ vzJwzzxwzyxzzxzzpzzhzz`zzTzzLWzESzJPzOQzSRzWSz_Tzb\ UzfzzjzzmzzjzzgzzdzzbzzezzhWza`zVezOjzHozAtz4rzFqz\ Ppz_oziazVPzHCz3Bz2Bz2Bz2 } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|