FOTD -- February 20, 2013 (Rating 7) Fractal visionaries and enthusiasts: The FOTD that appeared two days ago on February 18 was named "A Phantom Parent". In that image it is apparent that another fractal lies buried beneath the surface fractal, but because the surface fractal is critical, that hidden fractal must be forever obscured. But things are not nearly as bad as they first appear, for in today's image I take away the surface stuff and reveal that phantom fractal in its full glory, which explains the name "The Phantom Revealed". The trick lies in choosing the alternate critical value of initial Z. The generating expression actually has two critical values. In the previous image, the initial value of Z was automatically set to zero, one of the critical values. In today's image, I have reset the value of initial Z to -1, the second critical value. The result of this change is to move the previously buried fractal to the surface, and bury the fractal that was previously on the surface. Fragments of the previous surface image now appear as the bits of orangish stuff scattered about today's scene. Calculating complex critical values is not much fun. One of these days I might find a formula that can switch the critical values of initial Z automatically, but that day is not in the foreseeable future. Until then, I will continue to find the alternate critical values with the graphic method. The rating of a 7 totally reflects the mathematical value of the image. The artistic value hardly exists. But I will dive into today's image and post what I find there as tomorrow's FOTD. Who knows, I might find something worth a higher rating. Check the fractal phantom at: <http://www.crosscanpuzzles.com/Archives.html> With a deeper analysis at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And the spooks from the past at: <http://www.Nahee.com/FOTD/> Typical midwinter weather prevailed at Fractal Central today, with a temperature of 28F -2C and frequent but light flurries of snow. The fractal cat made a break-out but got caught before he got into trouble, and was soundly scolded for his efforts. The humans made it through the day with only one spat, which was due to FL's testiness. My patience, approaching that of Job, kept things under control however. The next FOTD will be posted in 24 hours. Until then, take care, and when will the over-zealous technophiles realize that technology cannot solve all of man's problems because it has created many of them itself? Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= ThePhantomRevealed { ; time=0:00:10.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=cosxx float=y center-mag=0/0/0.69 params=-2/2.3/1/4.6/-0.02/0/-1/0 maxiter=750 inside=0 symmetry=xyaxis periodicity=6 colors=000GSNTT_RVaQXbOZdNaeLdfKhhIliHpkFplEomCnoB\ mpAmq9mn8mk8kh7if7gc6f`6eZ5dW4cT4bQ3aO3`L2_I2ZG3YK\ 4XO4WR5VV5UYzmazmdzmezmfzmfzmgzmgzmbzmZzmVzmQzmMzm\ IzmIzmIzmIzmJzcJzcJzcJzcJzcJzcJzcJzcJzcJzcJzcKzcKz\ XKzXKzXKzTOzXKzWKzWKzWKzWKzWLzWLzWLzWLzWLzVLzVLzVL\ zVLzVLzVLzVMzVMzVMzUMzUMzUMzUMzUMzUMzUMzUNzUNzTNzT\ NzTNzTNzTNzTNzTNzTNzJOzLNzNNzPNzRNzLMzMNzMNzNNzNNz\ NNzONzONzPNzPNzPNzQNzQNzRNzRNzRNzSNzSNzTNzTNzgQyfP\ xfPwePwePvePudPudPtcPscPrcPrbPqbPpaOpaOoaOn`Om`Om_\ Ol_Ok_OkZOjZOiYOhYOhYOgXNfXNfWNeWNdWNzVNzVNzUNzUNz\ UNzTNzTNzBYzCXzDXzDWzEWzFWzFVzGVzHUzHUzIUzJTzJTzKS\ zKSzLSzMRzMRzNQzOQzOQzPPzQPzQOzROzSOzSNzTNzdWzaTzZ\ RzWPqqJppKooKonKnnKnmKmlKmlKlkKzjLziLziLzhLzgLzgLz\ fLzeLzdLzdMzcMzbMzbMzaMz`Mz_Mz_MzZMzYNzYNzXNzWNzVN\ zVNzUNzTNzx`zw_zv_zu_zuZztZzsZzrYzrYzqYzpXroXzoXzn\ WzmWzlWzlVzkVzjVziUziUzhU } frm:MandAutoCritInZ {; 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 PARAMETER FILE=========================================