FOTD -- November 25, 2002 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal, which mixes fractional parts of Z^(101) and Z^(-1.5), is a picture of another midget lying in a valley of its parent. And the parent is another indescribable fractal with a critical area filled with bits and pieces of Mandel- material, where the midgets are found. In response to these undeniable facts, I have named the image "Just Another Midget". I rated it at only an average 5. I know of no reason for the merely average rating. The colors might be a bit too brilliant, but fractals can look good with bright colors. I am simply dis-satisfied in some way. Why do I feel this vague dis-satisfaction with today's image? Nothing is wrong with midgets, (Minibrots, atoms). They are among the most interesting of fractal objects. But though their number is infinite, they comprise only a tiny part of the vast universe of fractals. Could I finally be becoming bored with midgets? A couple years ago I went an entire month without featuring a midget in the FOTD. Perhaps I need another such break. Perhaps I need to return to the preoccupation with four-dimen- sional figures and the curiosities of four-dimensional space that filled the FOTD discussions a couple years ago, when I posted many images of odd slices of the 4-D Julibrot figure. The Seahorse Valley area of the Mandelbrot set is perhaps the richest area of that best-known of all fractals. Its Julia sets are among the finest the M-set has to offer. But in addition to Julia sets, the four-dimensional Seahorse Valley area can be sliced to create Oblate sets, Rectangular sets, Elliptic sets and Parabolic sets. These less-familiar sets illustrate slices through Seahorse Valley in the remaining four mutually-perpendi- cular directions of 4-D space, and they are quite rich in an entirely new way. I think I will make December the month of the fourth dimension. The images will feature odd slices of the Z^2+C Julibrot, and the discussions will tell of the curiosities of 4-D space. Mini- brot lovers need feel no concern. When the new year arrives, the Minibrots will return, though not in the nearly exclusive manner of the past year or so. Today's image, which I have almost forgotten in my hyperspace ramblings, renders in under 10 minutes on my tired old fractal- workhorse P-200 machine. The file of the completed GIF image downloads in only a minute from one of the following two web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Sunday here in the Fractal Central part of the world was near perfect, with full sun, light breezes, and a tempera- ture of 59F 15C. The cats were happy and so was I. No treats were needed. Today is promising to be a repeat, except that I now have a pile of work before me. Actually, it's a virtual pile, since the work is contained on a computer disk. When the work is finished, the fractals will appear, and one of them will be the FOTD for tomorrow. Until that serene moment, take care, and beware of rogue fractals lurking in the shadows. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ JustAnotherMidget { ; time=0:09:35.84--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.71809236052173200/-0.114940189613520\ 40/88703.96/1/172.5/1.31302241301867184e-009 params=0.26/101/0.4/-1.5/0/0 float=y maxiter=1500 inside=0 logmap=73 periodicity=10 colors=0006PQ6P06Q06R0AS0FT0KU0PV0UW0ZX0cY0hZ0m_0r\ `1wa3x`2wZ2wY2vW2vV2uT1uS1tQ1tP1sN1sM0rK0rJ0qH0qG0\ mcwncvocvpcuqdurdttdsudsverwmrxmqymqxfpwmovgnummuh\ lthksijriiriinjfkkdhlbem_anYZoWWpTTqRQrPPpROnTOmVN\ kXNjZMh`MgbLedLdfKbhKajJ_lJZmK`jKahKceKdcKe`KgZKhW\ KiUKkRKlPKmMKoKKpHKqFKsCKtAKu7Kw5Kx2Ky0Mx1Nw1Pv1Qu\ 1Ru1Tt1Us1Vr1Xq1Yq1Zp1`o2an2bn2dm2el2fk2hj2ij2ji2l\ h2mg2ng2anRD3XC4XB5XA6X97X88X79X6AX5BX3DV4CX5CY6BZ\ 7B`8Aa9AbA9cB9eC8fD8gE7hE7jF6kG6lH5mI5oJ4pK4qL3rM3\ tN2uO2vO2w`JKaMMbPOcSQdVReYTf`VgcWhfYii_jl`koblrdm\ tehsadrZ`qWWpTSoPOnMJmJFlG6qCBkDbfELaEeXFhRGiMGiHH\ j7JiCHkGFpKEnOCpSBrW9s`7uc6wg4yn2xk3xh3xf4wc4wa4wZ\ 5wX5vU6vS6vP6uM7uK7uH8uF8tC8tA9t79w28t59r8ApABmDCk\ GDiIEgLFdOGbQH`TIYWJWYKU`LScMPeNNhOLkPImQGpREsSCuS\ EvVFwYHx_IybKzeLzgNzjOzmRzqPzoOzmNzkLzjKzhJzfHzdGz\ cFzaDz_CzYBzX9zV8zT7zR7zS } 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==================================