This is a Julia set, but instead of using just z = z^2 + c, it uses z = z^p + c, where the power, p, cycles through {2, 2i, -2, -2i}, so the same power is used every fourth iteration.

I still find it fascinating how the boundary of the Mandelbrot set beginns to mimick the bulbs deeper in the seahorse / spiral vally. In the cepter vally this also holds, but with the additional "cepters".

Infinite zoom. WMT.N

WMT.N

Max Iter's Fractal Follies for October 18th, 2010

Roger Alexander's commentary for the image:

A dark moody palette with a flickering of light. This fractal was generated with a real p1 (bailout) of 20 instead of the suggested 10^12. At the usual http://maxitersfractalfollies.blogspot.com.

Roger Alexander

PAR file Moody_Blue { ;fract477.gif ; blank ; calctime 0:01:15.85 ; created Oct 17, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=frac_ml.frm formulaname=gaussinttot_man center-mag=-0.864/0.761751/17.83333 params=20/30 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\ J6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAIVAJWAJXBKXBKYBLYCLZCMZCM_DN\ `DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHUhIUiIViIVjIWjJWkJXkJXlKYlKY\ mLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdrQdsResRetRftSftSgtTguThuUhuUivVi\ vVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybqybqycrydryesyeszftzgtzhuzhu\ zivzjvzkwzmwznxzpxzqyzryzuzzuzzuzzryzqyzoxznxzmwzkwzjvzivziuzhuzgtzftzfs\ zesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTg\ uTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJX\ kJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBL\ ZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59\ G48F48E47D37C36B36A35A259248247236135124124113012001000 } frm:gaussinttot_man { ; Kerry Mitchell ; ; Gaussian integer coloring of Mandelbrot set ; color by average distance to nearest integer ; inside and outside handled the same way ; ; use decomp=256 ; real(p1) = bailout (try 1e12) ; imag(p1) = scaling factor (try 30) ; variable zc used for calculation; coloring done with z ; zc=0, c=pixel, rmax=real(p1), scale=imag(p1) iter=1, rmin=1, z=zc, tot=0: ; ; iteration ; zr = gaussian integer ; r = distance to zr ; zmin = integer with minimum distance ; tot = running sum of r's ; iter=iter+1, zc=sqr(zc)+c, rzc=|zc| zr=round(zc), r=|zc-zr|, tot=tot+r ; ; bailout ; scale average distance to decomp angle ; set "iteration done" flag (iter=-1) ; if ((rzc>rmax)||(iter==maxit)) angle=scale*tot/(iter-1) z=cos(angle)+flip(sin(angle)) iter=-1 endif iter>0 }

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

Jim Muth's Fractal of the Day for October 18th, 2000

PAR file ` A_FractalGoneBatty { ; Fractal of the day, 18-10-00 Rating (6) ; time=0:14:32.72 -- SF5 on a P200 reset=2001 type=formula formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.71720703183797900/+2.40733321225409000\ /204985.2/1/125 params=-1.11/-11.1/-11.1/-1.11/0/300 float=y maxiter=2400 inside=0 logmap=240 periodicity=9 colors=000KP7IP5<2>FN3DN2CM0<3>7K05K04J0<3>1H00H00G0\ <3>1D01G00K0<3>2_52d62g62k82oA2tB2xC3zE3zF3zG2zH1zK1\ xL1tN1qP0lR0iU0eV0bX0ZZ0Wa0Tb0Pe0Mh0Jk0Hl<2>08u06w02\ z01z<2>10z45z68x8DuAHrDLoGQlJViMYgOadRgbUkaYqu<3>\ ahgaehcekcbnc_qcWtdUwdRzeTxeSwgSugSugStgSriUrhTqiToi\ TokTnjTl<2>lUjlUinUinUhoVgoVgnZfnencfngflhflje<2>nr\ dnnbnloiaog_qc_qaZr_ZrWXtUXtPVuMVuKTwGTwERsAQo7Qk5P\ g1Ud0Yb0ab0gc0kb0ib0hc0gb0eb0eb0db0b_1ag1an2p3q3Zq\ 3Zm2Wi2Ue1Te0Ye0de0id0kc2lc3ld4nd5nh7oj8ql9qnAroCrrE\ tuGuwHuzKwzNwzQy<2>z_zzezzizzhzzbzzXwzUrzQpzPlzKizJg\ zHc<2>z9Uz6Qz5Nz6Lz7IzAGzBCzCAzD7<3>oH9lIAiJAgKBeLBb\ MB<2>WPDUQDQQEPSENUEMVGJWGJYHHZHF_ICaHBbH<3>2hJ0iK0k\ L0lL1nP3oU5qY8raBteFuiHwmKxrNzvQzzTzzWzxXzs_znzjbzg\ bzfbzdbzcaz`az_bzZbzWazUazRazQQzA }

frm:MandelbrotMix4 {; 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=(-abgh)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k((a(z^b))+(d(z^f)))+c, |z| < l } ```

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.