FOTD -- September 03, 2003 (Rating 3) Fractal visionaries and enthusiasts: When I opened my e-mail box this morning, I found, among all the offers of more length, a letter informing me that I had just won 13-million dollars, or was it euros, in the European Lottery. This is strange, since I never bought a ticket. But I'm not questioning that aspect. The letter then asked for my bank account number so that the money I had won could be deposited in my account. I replied, requesting that the lottery commission send a check instead. As soon as the check arrives, I shall retire and devote the rest of my days to exploring the world of fractals. I wonder how long it will be before the check arrives. As for today's fractal, it is worth about as much as I am going to be enriched by winning a lottery I never entered. (Could anyone be gullible enough to actually reply to such letters?) I gave today's image a courteous rating of a 3. Actually, it might be closer to a 2. The image is so poor because I had no time to work on it. An unexpected rush job came in on Monday and kept me busy until after midnight. I'm still not quite caught up. Having no time to find a new fractal, I turned to one I generated yesterday, when I saw a message on the Fractint list that 7-armed spirals are a rarity in fractals. I had not realized that such spirals were rare, and to see if this were so, I went to a period-7 bud of the Mandelbrot set and drew the Julia set of that area. Then, for a bit of added interest, I double rotated the image 0.1 degree from the julia direction and got my 7-armed spiral, with a vague hint of Mandelbrot buds in the background. The picture had potential, but then the work came in and I had no time to color it properly. I leave the colors as they were when I had to stop working on it. I named the image "Spiral", and used it as FOTD for today. I might have done better not having a FOTD for today at all, but having gone this far, I am not going to scrap it now. The render time of 18 minutes is too slow for such a question- able image. I advise downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The Tuesday temperature of 84F 29C here at Fractal Central was fair enough, but there was little sun. The occasional sprinlkes of rain were not enough to wet a person, but made the grass too wet for the sensitive paws of the dynamic cats. As a result, they had a bad day and needed their evening treat of tuna to restore their good moods. Today is starting cloudy, cool, foggy, drizzly, with occasional sprinkles of rain. It is sure to be another bad day for the duo. For me, I've still got that left-over work to catch up on. So until next FOTD, take care, and don't get twisted up in an endless spiral. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Spiral { ; time=0:18:49.82--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=-0.344854/0.856196/4.523577/1/\ 70/-5.05012698326368081e-014 params=89.9/89.9/2/0/\ 0/0/0.36837/0.14068 float=y maxiter=50000 inside=0 logmap=yes periodicity=10 colors=000UFAUPAUFAUPAUFAUQAUFAUQAUGAUUAUJAUXAULAU\ ZAUNAUaAUOAUbAUPAUdAUQAUeAURAUcAUSAUbAUTBUaCUUDU`E\ UVFU_GUWHUZIUXJUYKUYMUZNUZOUZPUZQUZRUZSVZTWZUXZVYZ\ WZZX_ZY`ZZaZ_bZ`cZ`dZ_eZ_f_ZgZZh_YiZYj_XkZXl_WmZWm\ _VlZVl_UlZTk_TkZSj_SjZRj_RiZQi`QiZPh`PhZOg`OgZNg`M\ fZMf`LeZLeaKe_KdaJd`JcbIc`IccHbaHbdGacGaeFadE`fE`f\ D_fD_fC_fCZfBZfBYfAYfAYf9Xf9Xf8Yg7Xf8Xf9Xe9XeAXdAX\ dBXdBXcCXcCXbDXbDXbEXaEXaFX`FX`GX`GX_HX_IXZJXZKXZL\ XYMXYNXXOXXPXXQXWRXWSXVTXVUXVVXUWXUXXTYXTZXT_XS`XS\ aXRbXRcXRdXQeXQfXPgXPhXPiXOjXOkXNlXNmXNmXMmXMmXLmX\ LmXLmXKmXKmXJmXJmXJmXImXImXHmXHmXHmXGmXGmXFmXFmXFm\ XEmXEmXDmXDmS8mVBmXDmZFm`HmbJmdLmfNmhPmiQmjRmjRnjR\ ojRpjRqjRrkRskRtkRukRvkRwkRxlRylRzlRzlRzlSzlSzlSzm\ SzmSzmSzmSzmSzmSznSznSznSznSznSznSznSzoSzoTzoTzpUz\ pVzpVzqWzqWzqXzrYzrYzrZzsZzs_zs`zt`ztaztazsbzrbzrb\ zqczqczpczpdzodzndznezmez } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================
----- Original Message ----- From: "Jim Muth" <jamth@mindspring.com> To: <fractint@mailman.xmission.com> Cc: <philofractal@lists.fractalus.com> Sent: Wednesday, September 03, 2003 9:05 AM Subject: [Fractint] FOTD 03-09-03 (Spiral [3]) <snip>
Having no time to find a new fractal, I turned to one I generated yesterday, when I saw a message on the Fractint list that 7-armed spirals are a rarity in fractals. I had not realized that such spirals were rare, and to see if this were so, I went to a period-7 bud of the Mandelbrot set and drew the Julia set of that area. Then, for a bit of added interest, I double rotated the image 0.1 degree from the julia direction and got my 7-armed spiral, with a vague hint of Mandelbrot buds in the background.
Hey, I didn't *state* that 7-armed spirals were rare! I *asked* if this were so. Since you were able to produce one on demand, I guess the answer is that they are *not* rare. My 7up, however is a much nicer spiral, with another somewhat intriguing feature...I thought. If I back away some distance from my screen, I see that the sub-elements of the slowly spiralling arms form another spiral...a much faster spiral, (shorter pitch). Something that was discussed in Philofractal back in May and June...I have been surprised by the lack of comment in "Scientific American" regarding the multiple universe article by Max Tegmark. Well a few letters have finally surfaced. It was my own belief that this whole thing was built upon flawed reasoning which led to paradox. One reader pointed out an omission in the boundless possibilities suggested by Tegmark...a theism. I guess that this reader is thinking along the same lines that I followed; "Space appears to be infinite in size. If so, then somewhere out there, everything possible becomes real, no matter how improbable it is". Therefore there's a universe somewhere which is built and managed by "God". John W.
participants (2)
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Jim Muth -
John Wilson