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.

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.

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=========================================