FOTD -- February 22, 2005 (Rating 7) Fractal visionaries and enthusiasts: In the northern hemisphere today is the first day of autumn. In the southern hemisphere it is the first day of spring. At 2223 GMT the sun stands directly over the equator somewhere not too far south of Hawaii. For a brief moment, everything is in balance, the great world fractal is motionless, and it is said an egg will balance on its end. This might be true in some parts of the world, but not here at Fractal Central. The only way I can make an egg stand upright is to place it on a flat surface and prop it up with a few grains of salt. The big question would seem to be how the story got started. It is also said that the entire universe might be a fractal, which would mean that eggs are fractals also. But there is nothing egg-like in today's striking image. Today's fractal is part of the larger fractal that results when the formula Z^(1.1892)+C is iterated at ground zero level of the logarithmic spiral. Actually, I should say 3.14159 levels down the complex logarithmic hyperspiral spiral, for the number pi is actually best considered ground level of the spiral. (I might write another formula, one that correctly sets ground level.) The exponent of Z in today's image is 1.1892, and it is no acci- dent that this number is the fourth root of 2. I chose this value because the midgets are easier to find in fractals whose Z exponents are roots of 2. I really did not need to choose a root of 2 however, for I have discovered a simple method of finding those elusive hidden midgets in fractals with exponents of Z between 1 and 2. After giving today's image full consideration, I rated it at a 7. This is about the 6th consecutive rating of a 7, which is a sign that, at least in my opinion, I am on a fractal roll. The name "The Fourth Root" is a simple description of the exponent of Z. The render time of 2 minutes is thankfully brief. And as for those with Fractint-deprived machines -- they can see the image by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An absolutely perfect day (we sure have been having a lot of them lately) here at Fractal Central on Wednesday kept the fractal cats contented. Finishing the work early and finding a good fractal kept me contented also. Today is starting sunny and only the slightest bit cooler. It seems another good day is coming up. The next FOTD will appear in 24 hours. Until then, take care, and don't ignore the minutiae. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= The_Fourth_Root { ; time=0:02:05.01--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 periodicity=10 center-mag=+1.99538087334197200/+1.392766250999284\ 00/37712.73/1/-17.5/2.84751282275675e-009 logmap=55 params=1.1892/0/0/0 float=y maxiter=1500 inside=0 colors=000VTVTQTQOQOMTMKRKEOI7LH0HB0HD0OB7UHMZX_fl\ nnzzttlzlXzdHzX2zQ0zvazzzizzizzinqiaeiQViFKiXMvlOz\ zQzzTzzOzzMdqKHtIDvH9xH5xF2zF0zD0zD0zM2xXBveMtoXqz\ gqzqizvazxXzzOzzIzzBzz5zzBXzH0zM0zT0tY0dd0Qi0Bo00z\ 03z09z03q70eK0V_0In07z0Fz0Mx0Tv2_t5eqBnoHtoKxvMzzO\ zzQzzTzzTzzKzzDzz7zz0zz0zz0zz2zzFzzTzzzzztzznzzgzz\ azz3zz0zzlzzezzazzXzzTzzOzzIzzFzzBzzHzzKzzIzzIzzIz\ zlzzzzzlzzKzzQzzV0zY3zaBzgKzlTzo_ztQzxIzzBzz3zz0zz\ 0zz0zz0za0z00z30z90zD0zI0zM0zBBz0Tz0iz00zT0zK0zD0z\ 70z00z02z0Qz0nzDzzQzzVvzYnzaezdYzgQzlIzoDzqDzzDzzD\ zzHzzIzzMzqOziQzdIzaDza5za0za0za0za0za0zO0zB0zO0za\ 2zo3zz0zz0zz0zz0zz0zz_zzgzznzttzdzzOzzBzzDxzDtzFoz\ FlzHgzHdzIazIYzHXzFVzFQzDOzDMzBKzB9z20z00z00z0zzMg\ z29z0zzXzzXzz0vz0ez0Oz39zF0zQ0za0zF0z07z0Kz0Yz3lzI\ zz_zzozzazzOzzBzz0zz2zz5zz9zzDzzHzzKzzOzz_vzioztgz\ zazzXzzVzzVzzVzzvzYozYizY } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================