Fractal visionaries and enthusiasts:  

Today's image is named "Epsilon in Epsilon" for the same reason that yesterday's image was named "PI in PI".  Epsilon is an irrational number equally as important as PI, though its importance is more difficult to explain.  Epsilon is the base of the natural logarithm.  This is easy enough to state, but it is more difficult to explain why epsilon should have been chosen as a logarithmic base.  Among other advantages, epsilon simplifies the task of calculating logarithmic derivatives.

The image was generated by the formula Z^(e)+C as calculated (e) levels up the hyperladder.  This combination creates a parent fractal shaped like a Mandelbrot set with two period-2 buds and two East Valleys.  Today's scene lies in the southern East Valley.

The over-busy effect was achieved by rendering the image with the outside set to 'tdis'.

Both the art and math ratings are a normal 7.

The calculation time of 4 minutes is rather slow.  Thankfully, the web sites will bring relief.

A cloudy but mild day passed unappreciated here at Fractal Central.  The temperature of 66F 19C was actually a couple degrees above normal for early October in Central Pennsylvania, but both the fractal cats and fractal humans were occupied with too many other things to enjoy the mildness.

The next FOTD will probably be posted in 24 hours.  If not, it will appear in three days on October 12, since we, the fractal humans, will be back at old Fractal Central on the 11th.  Until whenever, take care, and I'm so worried about so many things that I'll have to run out and buy all the sponsors' products.

Jim Muth
jimmuth@earthlink.net


START PARAMETER FILE=======================================

EPSILON_in_EPSILON { ; time=0:04:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=Mandelbrot4BC passes=1
  center-mag=+0.2941099585792077/-0.2251101963909634\
  /1.059865e+010/1/162.5/0 params=2.71828182845905/\
  2.71828182845905 float=y maxiter=4500 inside=0
  outside=tdis periodicity=6 mathtolerance=0.05/1
  colors=000DX7A_07b04b01d00g00g04n07s0Dw0Fw4KwFNwNS\
  wXVwcZwnawufwuiwukwu0wXFwfXspnluiduaXuSQu8KuSEuSBu\
  DBuIBu3BuKBuKBu7Bu0Bu0Vu0Qu0Vu0wuwzzmmmKnu0Qn0BX00\
  F00000700F00N00S00Z00f00nABsABuABzA0KUBiNBuNBuNBuN\
  BuNBuNBuNJuNBuNBuKEuKKuKQuHVuH_uHdpFjiFnaFsVFwNDwF\
  Dw4Dw0Aw0Aw0Aw0Aw0Fw0Hw0Nw0Pw0Sw0Xw0Zw0cw0fw0iw0nw\
  0pw0uw0uw0uw1uw4uw7uwAuwDuwFuwHuwKuwKusXuBipBVsBXu\
  BZuBZuBauBauBcuBfuBfuBiuBiuBkuBkuBnuBpuEpuEsuEsuEu\
  uEuuHuuHuuKuuKuuNuuNuuNuuTuuXuubuuduujuunuuquuvuuw\
  uuwuuwuuwuuwuuwuuwuuwuuwuuwuuwuuwuuwuuwuuwuuwuuwuu\
  wuuwuuwuuwuswuiwuawuVwuKwuDwu4wu0wu0wu0wu0wu0wu0su\
  0Xu0_u0bu0du0gu0ju0lu0nu0nu0qu0su0vu0wu0wu0wu0wu1w\
  u7wuAwuFwuHwuNwuPwsVwiXwaawScwKiwAkw1pw0sw0uw0uw0u\
  w0pw0kw0fw0aw0Xw0Sw0Nw0Hw0Dw0uquZBuuKcuj0ul0ul0un0\
  un4uqDuqKuqSusZusfsvpnvuiwucwuZwuVwuPwuKwuFwuDwupd\
  nuH0uN0uQ0uV0KQXHTSFVKFVD }

frm:Mandelbrot4BC   { ; by several Fractint users
Z=C=Pixel:
Z=log(Z),
IF(imag(Z)>0),
Z=Z+flip(2*PI), ENDIF
Z=exp(real(p1)*(Z+flip(imag(p1))))+C,
|Z|<36 }

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