;     Date: Thu, 07 Aug 2014 20:23:32 -0400
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 07-08-14 (The FMOD Cycle [A-7,M-8])
;       Id: <1.5.4.16.20140807202520.38079cf2@earthlink.net>
; ---------
; 
; FOTD -- August 07, 2014 (Rating A-7,M-8)
; 
; Fractal visionaries and enthusiasts:
; 
; NEW FORMULA!!
; 
; Today's formula is another new one.  Forget about the ersatz 
; 'new' formula posted on August 4th, which has already been 
; discarded.
; 
; -------------------------------------------------------------
; BranchCutGen        { ; Jim Muth
; Z=C=Pixel:
; Z=log(Z),
; Z=exp(real(p1)*(Z+flip(imag(p1))))+C,
; |Z|<36 }
; -------------------------------------------------------------
; 
; Given impetus by Hal Lane, I decided to see how much I could 
; simplify the BC formulas and still get the same fractals.  
; Today's formula is about as far as I could take the process.  
; When I analyzed the old formulas, I was surprised at how many 
; terms simply canceled out or had no effect.  Today's new formula 
; is the result.  The by-product is a 33-percent increase in speed.
; 
; I named today's image "The FMOD Cycle" mostly because the image 
; was rendered with the inside set to 'FMOD'.  The cycle part of 
; the name refers to the complex logarithmic hyperspiral of the 
; Z^sqrt(2)+C fractal, which, starting at zero, repeats every 
; 4.442... levels.  Today's image is located 2.221... levels up 
; the hyperspiral, which is exactly halfway back to the starting 
; point and produces a parent fractal with X-axis symmetry.
; 
; The art worth of the image impresses me as a 7; the math rates 
; an 8, which is perhaps overblown.  After all, the basic math is 
; old stuff.  Only the streamlined formula is new.
; 
; Today's image is the actual parent fractal, made somewhat 
; unrecognizable by the 'FMOD' inside fill.  This is why it 
; calculates in a matter of 22 seconds.  If this is still too 
; slow, the web sites can make things a bit speedier.
; 
; Check the finished images at:
; 
;       <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>
; 
; A mix of puffy clouds and blue sky, a temperature of 79F 26C, a 
; passing afternoon shower, refreshing low humidity, and a gentle 
; north wind made today a day worth waiting for here at Fractal 
; Central.  The fractal cats missed much of the day when they 
; slept all afternoon.  The fractal humans had an uneventful 
; though busy day.
; 
; The next FOTD will be posted in the appropriate time.  Until 
; whenever this might be, take care, and the governments tell the 
; people what they can and cannot do, the big corporations tell 
; the governments what to order the people to do, but who tells 
; the big corporations what to tell the governments to order?
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

The_FMOD_Cycle { ; time=0:00:22.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=BranchCutGen center-mag=-0.0840312/0/\
  0.778816/1/0 params=1.414213562373/2.22144146907933
  inside=fmod float=y maxiter=1500 symmetry=xaxis
  proximity=0.049 periodicity=6
  colors=000MCcLCbKBaKB`KB`JB_JBZJAZIAYIAYIAXHAWH9WH\
  9VG9UG9UG9TF8TF8SF8RE8RE8QE8QD7PD7OD7OC7NC7MC6MB6L\
  B6LB6KA6JA5JA5I95H95H95G84G84F84E74E74D74D63C63B63\
  B53A5395294284284273263163152142142131031021010010\
  00cGFbFEaFE`ED_EDZEDYDCXDCWDCVCBUCBTBBSBARBAQAAQA9\
  PA9O99N98M88L88K87J77I76H76G66F65E55D55D54C44B44A4\
  3933833722622522411311211100000ol5mj4li4jg4if4ge4f\
  c4db4f`ngangbngcngdngengfnggnghnhinhjnhknhlnhmnhnn\
  honhpniqnirnisnitniunivniwnixngvlftkericqhcpgbofam\
  e_kcZjbYh`Wf_VdYUcXSaWR_UQYTOXRNVQMTOLRNJQLIOKHMIF\
  KHEJGDHEBFDADB9CA7A8687565354232111shJqfIoeHndHlcG\
  kaGi`Fh_FfZEeXEcWDaVD`UCZSCYRBWQBVPATNASM9QL8OK8NI\
  7LH7KG6IF6HD5FC5EB4CA4A83973762652431321110kyYiwXh\
  vWgtVfsUerUdpTcoSbmRalR`kQ_iPZhOYgOXeNWdMUbLTaLS`K\
  RZJQYIPXIOVHNUGMSFLRFKQEJODINCHMCGKBEJADH9CG9BF8AD\
  79C68B6795684563453342221 }

frm:BranchCutGen        { ; Jim Muth
Z=C=Pixel:
Z=log(Z),
Z=exp(real(p1)*(Z+flip(imag(p1))))+C,
|Z|<36 }

; END PARAMETER FILE=========================================
; 
; 
; 
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