FOTD -- December 04, 2013 (Rating A-9,M-9) Fractal visionaries and enthusiasts: Today's superior image shows a minibrot in the parent fractal that results when the expression Z^(1.333)+C is iterated one level up the hyperladder with no function applied. This parent fractal rather resembles the eastern half of the main bay of the Mandelbrot set, complete with a quite convincing large quadratic bud on its northern side. Today's unusually brilliant scene features a minibrot lying on a tiny disconnected filament fragment near this almost-quadratic bud.
From a distance, the minibrot in today's image is shaped strikingly like the countless Minibrots found in the M-set, though a closer check reveals huge differences. The name "Pseudo Quadratic" refers to this false resemblance.
In my opinion, both the art and the math aspects are worth the rating of a 9. The art rating reflects the extra effort required to achieve the brilliancy. The math rating is so high because I have never seen a minibrot so closely resembling a quadratic minibrot in a fractal with an exponent of Z as low as 1.333. The calculation time of 4-3/4 minutes is admittedly slow, but at least in today's case, the result is well worth the wait. The finished image is or soon will be available on the following FOTD web sites: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Fine early winter weather prevailed here at Fractal Central today. The day began with heavy fog, but the fog lifted in the morning and revealed a mostly sunny sky that remained that way through the afternoon. The ample sun raised the temperature to a high of 48F +9C. The fractal cats appeared too interested in each other to pay much attention to the sun on the window shelf. The fractal humans had other things to do. The next FOTD will be posted in the proper time. Until whenever, take care, and which is worse -- conservatives who want to pass laws to force everyone to obey the rules of behavior set down in their Bible or liberals who want to pass laws to eliminate the natural inequalities inherent in humanity? As I see it, neither of these goals is ever going to be achieved, but it sure is a lot of fun watching the two sides continue their futile squabbling. Jim (neither right nor left) Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Pseudo-Quadratic { ; time=0:04:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.3243347326496687/+1.081261598206034/\ 3.441011e+009/1/172.5/0 params=1.333/0/1/0 float=y maxiter=5000 inside=0 logmap=-305 periodicity=6 colors=00000B00C00D00E00F10G20H30I40J50K60L70M80N9\ 0OA0P50G50H50I50J50K50L50M50N50O50P50Q50R50S60T70U\ 80T80T71S72S63S64Q53P53O42M40J30H30D208204100zQKtJ\ KqAKn8Hj8Dh46g60hB0iH0jL0kP0lT0mX0ma0ne0oi0pm0qq0z\ zFzzcVbB7HL6KK6MJ6OI6RH5TG5VF5YE5_D5aC6eD7iD8lD9pE\ AsEBwEBzEIyKPyQWyWbyaiygoylmvjkthjrfhpdfnbel`ciZbg\ X`eVZcTYaRW_PVYNTWOSVORTOQSPPQPOPPNNQLMQKKQJJRIHRH\ GRGESFDSECSJJWOQ_TXcYcgbjk`il_hmZhmYgnXgoWfoVfpUeq\ TeqSdrRdrOZzMTzJOzHIzECzC7zDCzDGzEKzEOzFSzFXzG`zGd\ zHhzHlzHpzIqzJqzKqzLqzMrzMrzNrzOrzPszQsXQsVRsSStPT\ tNUtKctImmKzmMzmOzmQzmSzmUzmWzmYzmZzmZzmZzmZzmZzmZ\ zmZxmZymZtmWomTjzRezOczMczJczHczEmzCmzJmzQmzXmzcfz\ jmzgmzemzbmz`mzYozWqzUszRuzPwzMzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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=========================================