FOTD -- April 18, 2002 (Rating 7) Fractal visionaries and enthusiasts: I named today's image "Ensign". I had no real reason for giving it such a name -- with as much as I have to do, I simply could think of nothing better. I rated it at a 7, which I believe is the highest rating to have been given a FOTD since I cut the FOTD schedule to one every 3 days. (When the CD is ready, the FOTD will return to its normal every-day schedule.) The parent fractal was created by the simple formula: -5(Z^(-1.1))-8(Z^(-11))+(1/C), a formula that creates a grossly oversized double-negative fractal. As is the case with many of these oversized double-negative fractals, most of the interest lies relatively near the origin, where the fractal takes on a critical appearance. Most of today's parent fractal appears to be a non-critical area where midgets are unlikely to be found, but there is the usual small area of interest near the origin. The point I chose to check for midgets lies at the end of a filament extending from a mandel-shaped bud. Of course, in fractals the filaments have no end. No matter how close the zoom-in point lies to the 'end' of a filament, by the time a midget is reached, the image has been magnified so much that a near infinity of even smaller midgets can be seen lying farther out on the filament. The trick lies in finding a midget that is close to but not beyond the limit of resolution. As a matter of passing interest, starting with a bloated parent fractal thousands of times the size of the default screen does not give a greater range of sizes to explore. The large size merely shifts the decimal point to the right without increasing the range of precision. Today's render time of just under five minutes is worth the satisfaction of doing it for oneself. Those who are already satisfied with themselves can find the rendered image posted to the two FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather here at Fractal Central Wednesday was ridiculously hot. The blazing sun and incredible afternoon city temperature of 102F 39C made life on the porch far too uncomfortable for the cats, who passed the heat of the day lying under the air conditioner, trying to catch as much cool air as possible. While the cats were trying to keep cool, I spent the day trying to get as much work done as possible so that I can advance the FOTD CD, which is progressing but still has a way to go. (Those who claim that I will never finish the CD will be given ample chance to eat their words when the disk is ready.) As for me, it's hot again today, the cats are already testy, and I've got a pile of work to get out of the way -- or at least to start. So until next time, which will be on April 21, take care, and be where the action is, but don't become a casualty of the action. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Ensign { ; time=0:04:42.81--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-2.53422952923341000/-2.428182368486123\ 00/5.617065e+007/1/62.5/1.20480510572285038e-006 params=-5/-1.1/-8/-11/0/0 float=y maxiter=900 inside=0 logmap=88 periodicity=15 colors=00070E80EA0EB0ED0EE0EG0EH0EJ0EK0EM0EN0EP0EQ\ 0ES0EV1EY4E_7JbAMeDQfGViJYlMbnPeoTfoXfq`hqchqhirki\ rokrrkvvrzzrzzzzzzzzzzzzlzrezuXzxPtzGoz8kz1fz0ez0e\ z0Tz0Jq18e10THzzNznSz`XzPbzBfz0kz0cz2XlJQY_oqbzzez\ zczxbzr`zl`wf_t`YoVXlPXiJVeDTb7S_1SS0`M0hG0o80x20z\ 00zzz0zz0zz0zz0xz0tz0qz0nz0kz0hz0YuTPrzNtzNuuNwrMx\ nMzkMzfKzbKz_KzVJzSJzNJzJHzGHzBHz8XAzVDqTGcSJQ7T`0\ ck0Tf8JcJ8`P5iT4q_2xc1zh0zT8rEGY0PD0X00_00b02e08h0\ Ek0Jn0Pq0Vt0_w0ez0iz0`z5TzBMzHEzN7zT0z_0ze7nTKbJYS\ 8kG0x50oB2fHGYNTQSfPVhNXhMYhK_iJ`iHciGeiEfkDhkBikB\ kkGihJifNieQicTibYi``i_ciYhiXkiVniToeQq`PrXMrSKtPJ\ uKGuGEwBDx7Az58z77z84zA2zB1zD2zE2zH4zK4zN5zQ5zT7zX\ 7z_8zb8zeAzhAzkAwnBtqBqtBnwBkzDhzDezDczDYzMXz`XzBP\ zHHzNAzS2zY0zc0zhVznQzhKzPQzKVzH`zDez8kz4oz1uz0zz0\ zz0zz0wz0iz1Yz8KzH7zP0zX0zS0zN0zK0zG0zD0z80z40z10z\ 00z00z00z02z0Bz0Kz2Tz8bzE } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================