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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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|<a } END PARAMETER FILE=========================================