FOTD -- January 26, 2002 (Rating 5) Fractal visionaries and enthusiasts: Fractals are pretty pictures that result when certain things are done with numbers. Some see fractals as art, others see them as mathematical graphs. I try, with only some success, to present fractals as both. I named today's image "Domain of Numbers" in recognition of the fact that fractals are made of numbers in much the same way as physical objects are made of atoms. (I'll not involve myself at the present with the fact that atomic particles are best represented by numbers, but it's a curious similarity.) Today's image was created by the formula Z^(-1.7)+0.1(Z^(-17))+(1/C). Forty years ago, who would guess that such a simple expression could produce such an intricate image. Back then, some mathematicians realized that Julia sets exist, but their appearance remained a mystery until the arrival of high-speed computers in the early 1980's. Like many of the old-timers in the world of fractals, I discovered the images around 1985, when I read an article about the Mandelbrot set in the Scientific American magazine. A year or so after that, a second article appeared, which set me firmly on the path of fractal exploration. Almost 20 years later, that initial enthusiasm has not waned. Today's image rates an average 5. It is a good representation of the average fractal that appears on the screen of my fractal machine. The render time of just under 17 minutes is a bit slow for an image that is only average. For relief, I suggest a trip to Scott's web site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> from where the completed GIF image may be downloaded. The fractal weather Friday was sunny with happy cats. Warm sun and a temperature of 52F 11C brought out the best in the fractal cats, who spent several hours in the yard doing whatever cats do in yards. The wind was a bit too brisk for the day to be considered perfect, but it was the closest we've come in over a week. Today promises to be even closer to perfection. And I've got the work just about caught up. It should be another great day for the dynamic duo. Check back in 24 hours to see just how perfect the day turned out. The next fractal will also be ready by then. Until I return, take care, and see you then. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Domain_of_Numbers { ; time=0:16:53.16--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.21134959886444100/-0.057343241946476\ 36/1.883642e+010/1/-99.9938442053906584/-0.0099007\ 0871181482348 params=1/-1.7/0.1/-17/0/0 float=y maxiter=1800 inside=0 logmap=279 colors=000fevbfwYizUkzQnzMqzIrzHnzFjzEfyDbvB_sAXr8\ So7Om6Kk4Ii3Ef2Ae06b03a68ZDEYJJVQOUXURaZQgcNniMunJ\ zsIzwHzwVzwizwwzwzzwzzwrzwizw_zyRzzJzwJuuJqsJkqJfn\ JbmJYjJSgJOfJJcJFbJHZIJXILUINRHQPHSNHUMHXJFZFF`BFc\ 6Ec3Ed0Ec0Ee0Dg0Bi0Al08m07o06r04u03w02z00z00z00z47\ uEFoOOjYXegc_qmVzuQzzYzoezcmwSusHzo4zk0zf0zb0vZ0qV\ 0mR0iN0eJ0_F0XB0S70N30J00F00B00F00J40NB0RI2VO4ZV7a\ _AZacXazUYzSVzQRyOOvMMsKIrIFoHDmE8jD6gB3fAKVAaKArA\ Az0Dz0Fq2Hi2J_3MS4NJ4QB6S27U07S0DR6IQBMOHRNMVMR_KX\ eJaiIfnHkrKiqNgqQfqScqVbqYaq_ZqbYqeXqbYsaZu__vZ_wX\ ayVbzUbzSczQezOezNfzMgzKgzNfzQezScwUbsXaoZ_k_ZgbYc\ eX_fVXiUSkSOmSMBcOJgQRmRZgRfSSnQUvOUoRYiS_bUcXXfQY\ jJZmE_oKamRajYaicafjacqabwa_zaYzaXzcYzeYzfYziZzjZz\ kZzmZzo_zq_zr_zs_zkXzeUzeRzfOzgKziIzjFzkDznAzq7zs4\ zv2zy0zz0zz7zzIzzSzzbzzkzzZzzMzzOzzQzzSzzUzzVzzYzz\ Zzzazzbzzczzfzzozzrzzszzu } 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==================================