; Date: Wed, 04 Dec 2013 16:07:26 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 04-12-13 (Pseudo-Quadratic [A-9,M-9]) ; Id: <1.5.4.16.20131204160723.2b4fe50e@earthlink.net> ; --------- ; ; 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: ; ; ; ; ; ; ; ; ; ; 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|