Fractal visionaries and enthusiasts: 

Today we apply the cotangent function to the Z^(PI)+C fractal and calculate it PI levels up the hyperladder.  The result is a fractal that closely resembles the 'true' PI fractal, though it is skewed and rotated a bit to the right.

Today's 'mammoth' minibrot lies near a much larger minibrot in a tiny disconnected bit of debris just north of the negative X-axis of the parent fractal.

The rating of an 8 indicates that I consider the image to be an improvement over previous PI fractal attempts.

The name "Cotangent PI" tells where the image came from.

The calculation time of 4-4/5 minutes is disagreeably slow, but the image is worth it, at least IMO.

The day here at Fractal Central began with low clouds and fog.  The fog and clouds cleared away by late morning, leading to a very pleasant afternoon with lots of photoshop (aka Kodachrome) blue sky decorated with the puffy white clouds that make a picture postcard so picturesque.  The temperature of 81F 27C just made things better.  The fractal cats had a relaxing day basking in the tiny sliver of sunlight that is just starting to come in their window as the sun angle grows lower.

The humans had an uneventful day.  FL still feels a bit triumphant over yesterday's victory in our little disagreement.  I let her feel she had won, while still claiming a morale victory for myself however.  The next FOTD will be posted when the right time arrives.  Until whenever that might be, take care, and fight for what you know is right, but when you find it is wrong, be ready to switch.

Jim Muth
jimmuth@earthlink.net


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

Cotangent_PI       { ; time=0:04:50.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=cotan
  center-mag=-0.6484451764762189/+0.1809410427501681\
  /1.650617e+010/1/135/0 params=3.14159265358979/0/\
  3.14159265358979/0 float=y maxiter=5000 inside=0
  logmap=470 periodicity=6 mathtolerance=0.05/1
  colors=000JOqJOqJOqJOqJOqJOqJOqJOqJOqJPqJQqJQqJSqJ\
  TqJUqJWqJWqJXqJYqJ_qJ`qKaoLbmMckNciOdhIdfDfd7hf3ih\
  2ki0mj1ik1gm1fm2co2ao3`q3Ys3Xs4Vt4St4Rv4Pv6Ox6Mz6K\
  z7Jz8Hz8Gz9Gz9EzACzABzAAzU9zC9za9ze9zK8zN8zi8zV8zd\
  7zW7z_7zb6zm6zj6zg6zj5zn5zs5zn5zt6zr6zr6zp6zp6zn5z\
  m5zl6xi6vj6tg6sg7qf6of6oj9kk9ihAfdBdaDa_E_XEXUHVRI\
  SPPQMLNLLLKKKJKKHNKEWHDSHCTF9VE7YC6_B4`92d81f74hB6\
  iD9iGAkIDmMGmOIoSKoUNqXQs`RscVtfYti_micxodjmhqqjst\
  ctnVfbSmYKaPHfJBcC2k48f79Q6GYAKVBPWDQPGMYJSQLTUMTS\
  PVURVTTXXXXXXYZYdadhhhloqnpqktzpszuzzvzzzzzzzzyzwl\
  omShUK_YCTS5GO0EG08F09I0EG0IN0MQ0OS1SX3VY4Y_6aa8dc\
  Bek9fd8f_7hW6iR6kM6kI5mE4m93o62o22q15q28q2Bq2Eq2Iq\
  2Mq2Pq2Tq2Xq2`q2bq2eq2gq2jq2nqCqqOqqaqqpyzixzYxz`w\
  zQvzOwzMvzLvzKvzIvzHvzGvzFvzEzzCzzCzzAzzCzzEzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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|<a }

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