FOTD -- May 04, 2003 (Rating 7) Fractal visionaries and enthusiasts: As I said in yesterday's FOTD, during the month of May I will restrict my fractal explorations to a single fractal -- the fractal that appeared as the FOTD for May 3, which was yesterday. I am doing this because in my continuing haste to find ever more fractals, I rarely stay with a single fractal long enough to become familiar with its various parts. And this parent fractal that I have chosen for May is one of the most varied I have yet found. Today we take our first venture into the parent fractal for May, which will serve as the parent of the FOTD images that will appear during the rest of the month. Today's image is located in the area where the edge of the large fan-like element merges into the 'East Valley' area of the obvious Mandel-shape on the right. I have named the image "Sargasso Seaweed". I gave it this name because something about it reminds me of rafts of seaweed lazily floating on a nearly calm ocean. But I could easily have given the image a name such as "Holey Iterations", since it has more holes than one can shake a golf course at. These holes are not Mandelbrot midgets, nor are they Julia sets. In fact, I don't know what they are, except just plain 'holes'. Such holes often appear in images created with the MandelbrotMix series of formulae. They also appear in certain parts of some fractals created with the MandelbrotBC1 formula, which draws the more remote levels of the fractals that contain a fractional power of Z. Today's image undergoes some curious changes when the bailout radius, which is the imag(p3) parameter, is raised to a sufficiently high value. These changes are the beginning of fractal 'evaporation'. They appear suddenly and unexpectedly. Finding the exact point of the beginning of fractal breakup is a challenging task, though in some cases, worth the effort. I used the MandelbrotMix2 formula to create the parent fractal for May, as well as all images that will appear during this month. This formula works exactly like the MandelbrotMix4 formula except that it has two additional changeable parameters, which can be used to change the starting point of Z. After studying today's image for all of 5 minutes, I decided that it was worth a rating of an above-average 7. The render time of 20 minutes, at least on my machine, is a bit slow, but relief can be found on the internet in the form of the completed image, which is or soon will be posted to the FOTD web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> On Saturday, good luck once again prevailed here at Fractal Central. There was little sun, but the rain held off and the temperature reached 63F 17C, producing conditions that any fractal cat would find enjoyable. Being fractal in nature, the dynamic cat duo thoroughly enjoyed their afternoon in the yard. At one time, the cat from two doors down made a brief appearance in the brush at the bottom of the yard. I think he was just trying to be friendly, but Tippy once again chased the other cat back down where Tippy feels he belongs. Today is once again threatening rain. Hopefully, the good luck will continue, and the rain will hold off. But there is no guarantee. Somehow, I got myself dragged into spending today looking at old junk at one of the local antique emporiums, so the duo will have to remain indoors until we return late this afternoon. Until next time, take care, and be ever more alert to signs of fractals in the world around you. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Sargasso_Sea-Weed { ; time=0:20:33.41--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.26815170075631500/-3.043295039151435\ 00/127119.9/1/70/1.31606140499340718e-008 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1500 inside=0 logmap=196 periodicity=10 colors=000h09g06f03e00d70cG0bI0aJ0`F0XA0V60T11Q03P\ 09L1S44JO6YA9TQAaICdQFiOGoHJpTLyQMuOLpFJn6IQLAOY4M\ j0Jx0Ip1Yj9mmDfoI`rMTsQOuVIx_Ayc4zg0zl0zp0zr0zs0yu\ 0xu0vv0ux0sx0py0oz0mz0lz0jz0iz0gz0cz0_z4VyAQvIMuPI\ sVDpa9oi4moFpjPrf_sa`uYavTbxPcvQdvSevSbvTSvTOxSLyS\ IzSFzSCzS9zSdzS1zSbzS0zS0xS0zS0tS0zQ0qP1rO6lMXgLFf\ JT`IO`GSVFPYFOXFL`FJcFIfFFjFDmF`pF9uFgxF6zFFY6MXFT\ XM`VTgV`oTgvTozTvzIxzOfzSPzX7z`0y_0uY0pX4mV9iTDdSI\ `QMYQP_JX`Daa6ic0od0uX0pO0lF1g73cD1aJ0aO0aT0aY0ac0\ ag0`m0`r0`x0`z0`z0`z0`z0cz0dz0fz1iz4jz7lzAmzDpzGrz\ JszMuzPxzSyzVzzYzz_uz`mzafzc_zcSzdLzfDzg6zi0zi0yf0\ yc0xa1x_4xX7vVAvSDuPGuOJuLMsIPsGTrDXrA_r9ap6dp3go1\ jo0mo0pm0sm0vr0zm0yj0xg0vd0ua0s_0rX0rOaFVaMacTia`g\ c_gcYgcYgcXgcVgdVgdTgdSfdSfdQfdPffPfgOfjMfmMfpLfsL\ auO_vQXxTSyXPz_MzaIzdFzgCzj7zm4zp1zs0zv0zy0zz0zz0z\ z0zz1zz4zz9zzDzzGzzLzzLzz } frm:MandelbrotMix2 {; 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)+(p4)), 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==================================