; Date: Thu, 20 Jan 2005 09:53:18 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 20-01-05 (Don't Square This [5]) ; Id: <1.5.4.16.20050120095533.29a78436@pop.mindspring.com> ; --------- ; ; FOTD -- January 20, 2005 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; Today's image pictures a tiny midget in the Z^(sqrt2)+C ; Mandeloid, calculated one turn down the log spiral. This is my ; favorite of all the Mandeloids with exponents in the range ; between 1 and 2. I enjoy exploring it especially because its ; midgets are far easier to find than those of other Mandeloids in ; this range. Whether the midgets are worth the search is another ; question. ; ; With an exponent of 1.4142..., the midgets have 1.4142... ; elements surrounding them in the outermost ring. In the next ; ring closer to the midgets there are (1.4142)x(1.4142), or 2 ; elements surrounding the midgets. Though these elements are ; broken, they usually create an obvious 2-way symmetry around the ; midget, which, just as in the Mandelbrot set, makes the midgets ; easy to find far before they themselves become visible. ; ; In today's scene the 2-way symmetry is clearly visible around ; the borders of the frame. Closer to the midget, the brilliant ; yellow-orange element has approximately 5.657 spiral arms ; attached, a number that happens to be 1.4142^(5). (We seem to ; have skipped past the powers 3 and 4.) ; ; The parent fractal of today's image consists of a Mandel-shaped ; main bay with a distorted bud on its north side. The image ; itself is located in a valley of a sub-bud on the northern edge ; of the large bud. ; ; I used the 'imag' outside fill when rendering the image to add a ; bit of life. In a way it adds a bit too much life. I would ; have preferred to see a little more organization. ; ; I named the image "Don't Square This". I gave it this name ; because if the exponent is squared, the result is the familiar ; Mandelbrot set, which is a totally different story. ; ; Though the midgets in the Z^1.4142... fractal are fun to find, ; I have yet to stumble upon one that is truly outstanding, as ; many of the midgets in the M-set can be. Today's image does ; have brilliant colors, but like all scenes in the fractals with ; fractional exponents, it leaves me with a feeling that there ; once was a great image here, but it broke up before I reached ; it. As a result, I can rate the image no higher than a 5. When ; the render time of 34 minutes is figured in, the overall worth ; comes to a 14.5, pretty low on the overall-worth scale. ; ; Things such as render times, values, and overall worths can be ; ignored by visiting the FOTD web site at: ; ; ; ; and downloading the finished GIF image from there. ; ; The enlightening philosophy about what we are and where we come ; from is still brewing, but it is not yet ready. Every time I ; check what I have written I find a few more things that seem ; to have not been clarified. I'll keep working on it until I ; get it right. Then the great revelation will appear on the ; philofractal list. ; ; Snow fell most all day Wednesday here at Fractal Central. By ; the time it ended 2-1/2in or 6cm of the white fluffy stuff had ; piled up. The temperature never rose above 23C -5F, making ; things far too unpleasant for the fractal cats, who took only ; one glance out the back door before deciding that the best way ; to pass the day would be to watch the snow fall from their shelf ; by the window. They seemed happy enough, and only the usual ; amount of tuna was needed in the evening. Today is starting ; cloudy and continued cold, with the ever-present threat of more ; snow. So far the cat duo seems happy enough, but the day is ; young and a lot can happen in 12 hours. ; ; For me, it's finish the work first and then move on to the ; fractals. Until the next FOTD appears in 24 hours, take care, ; and could fractals, which have no mass, escape from a black ; hole? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Dont_Square_This { ; time=0:34:19.32--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+0.24938287158000390/+1.427995501755636\ /4.643115e+008/1/100/-1.81791574210832252e-007 params=1.414213562373/0/-1/0 float=y maxiter=4000 inside=0 outside=imag logmap=1036 periodicity=10 colors=0000rz0pz0nz0lz0jz0hz0dz0`z0Xs0Uh0P_1IO5CCA\ 51H00D00C0092074447929D0AI0CO0DU0IX0M`0Rd0Wf1`j1do\ 2jp2nu4ty4yz7tyApyClyFhyHdyK`yNXwQUwQPwSMwSIwUFwUC\ uX9u_5ub2ud0uh0uo0wj0uh0ff7WbFI`M9_W0Xb0bW0fO2jIAo\ CHu5Oy0Xz0dz0lp0f`0bN0_A0W00S00O00O00K04I07H0CF0FC\ 4IA9O9DR7IW4O`2Ud1jt4_h0O_0DP05H009000000000000000\ 000002005507A09H0AO0CU0F`0Hf0Io0Ku0Mz0Oz0My2Ko7KdA\ IWFIOKHFOF7UF0_D0bD0_A0X70W40U00S01O04N07K0AI0DH0F\ D0CA09905502200100000000200700C02H05N0AS0Db0OX0HS0\ AN94HI0CR0AW09`07d05h05l04p02t11y40zA1z72p44d15U07\ I0990A00400800A42A2HKHXUWocazmjzwkuzfhzaXzgOzhHzmC\ zw7zz2zz0zz0zm0zc1zX2zR4zM5zH7yC9y99dD5OH47O10W00_\ 00f00z10h40b70XA0RD0OH0KK0IO0FS0DW0C_0Ab09f07j05o0\ 2s00w00z00z00z00z00zN_zQXzSWzUUzXRz_Pz`OzbMzfKzhIz\ jHzoFzpDzsCzu5zwCzyIzzOzzWzz`zzhzznzzwzzzzzzzzzzzt\ zz`zzHzz0zz4zz5zzfzzhzzhz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(p/(2*PI)) r=real(p2)-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|