; Date: Tue, 15 Jul 2008 19:11:53 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 16-07-08 (Naturally Fractal [7]) ; ; Id: <1.5.4.16.20080715191215.2af715e8@pop.mindspring.com> ; --------- ; ; FOTD -- July 16, 2008 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; Today's image returns us to the complex logarithmic hyperspiral, ; which we have not visited in about a month. The parent fractal ; was created by the formula Z^(1.875)+C as it appears 33 levels ; up this abstract spiral when the 'floor' function is used. This ; parent resembles a ragged, somewhat squashed Mandelbrot set ; rotated so that its main spike points northeast. ; ; I chose the exponent 1.875 because it is 7/8 of the way from 1 ; to 2, which is close enough to 2 to create minibrots resembling ; recognizable quadratic ones, yet far enough from 2 to create ; fractals of infinite variety. ; ; Today's scene is located in a filament extending from the ; period-5 bud on the southwest shore line of the large minibrot ; on the main spike of the parent fractal, very near the point ; where the hairline filament emerges from the chaos. ; ; I named the image "Naturally Fractal" in recognition of the fact ; that nature is filled with and possibly made of fractals. I ; rated it at a 7 because it not only leads to pondering, it also ; is attractive in its own way. And no one will complain about ; the calculation time of a mere 30 seconds. ; ; For added convenience, the finished image is posted for fast if ; not instant viewing on the FOTD web site at: ; ; ; ; Another perfect midsummer day went unrecognized by the fractal ; cats of Fractal Central on Tuesday. The temperature of 86F 30C ; was made quite bearable by the low humidity. My day was a bit ; too busy for total enjoyment, but I still managed a half-hour ; under the mulberry tree, pondering the mysteries of the outer ; world and man's pathetic efforts to comprehend it. The next ; FOTD, which BTW is still a mystery, will be posted in 24 hours. ; Until then, take care, and fractals can cause deep thinking. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Naturally_Fractal { ; time=0:00:29.98-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor center-mag=+1.298046570238266/+1.385392696646682/\ 1.09e+007/1/65/0 params=1.875/0/33/0 float=y maxiter=1200 inside=0 logmap=70 periodicity=10 colors=000OKOOKNOKNOKLOKKOKKOKKOKKOKKNKJMKILKEKKAJ\ J9II8HH7GG7FF6EA5B54814K46P77V99bCAgJCiHDzfCoJEzzD\ f3Fh0JimNj2Qk2Ul2Xm2`p1_n2cm2fl2ij3mi3ph3sg3va8uXc\ tSGsMLrHcrCTv1mz7mvCXrHWmMWhRWRWVL`VEdY3eV8fSCfPHg\ MLgJPiKRkKSmKUoKVzXNpKWb6og8dlAVqCKvEAzF0qO3iW5ad8\ UlAMdMEYYIZVMZTP_RT_PX_N_`Lc`Jf`HlRQrHYqMXpQXoUWnZ\ WmbVlfVqhPljVhl_cnd_oiVqnRssNtxHskBs_5rO0rC2cQ4Qc0\ Aw5CpAEjFGcE6XKHYPRYU`YswSZjY5eiEYbMQXUIQ`CGaAKa8N\ b6Rb5Uc3Yc1`c0cbDgaPk`ao_ms_ywfyjmyYtyLzy82i7czQ`r\ RZjSXbTVVUTOUTOUTOUTNTTNTTNTTNTTMTTMTTMTTMTTLTTLTT\ LTzLTzKTzKTzKTzKTzWkzTfzQazNXzgfzfeueetddscdrccqbc\ zabz`bz`az_azZazY`zX`zX_zW_zVZzUZzUYzzYzzXzRXzzXzQ\ WzzWzzVzzVzzUzMUVzTzzTzz2zz3Cz3Cz4zz4zz5zS5zz5zR6z\ z6Ez7Fz7Fz8zz8zz8zQ9Gz9zzAHzAHzBzzBzQBzPCzzCzPDJzD\ zPEJzEzPEzOFKzFKzGLzGLzHLzHLzHzzIMzIzzJzzJzzKNzKzz\ KzzLzzLOzMzzMPzNPzNPzNQzO } 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|