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Internet Message Format  |  1999-08-10  |  45KB
  1. From: owner-fractint-digest@lists.xmission.com (fractint-digest)
  2. To: fractint-digest@lists.xmission.com
  3. Subject: fractint-digest V1 #404
  4. Reply-To: fractint-digest
  5. Sender: owner-fractint-digest@lists.xmission.com
  6. Errors-To: owner-fractint-digest@lists.xmission.com
  7. Precedence: bulk
  8.  
  9.  
  10. fractint-digest        Tuesday, August 10 1999        Volume 01 : Number 404
  11.  
  12.  
  13.  
  14.  
  15. ----------------------------------------------------------------------
  16.  
  17. Date: Thu, 05 Aug 1999 17:34:30 -0500
  18. From: David Kosokar <dkosokar@mn.mediaone.net>
  19. Subject: Re: (fractint) Feigenbaum's Number
  20.  
  21. Feigenbaum's number = 4.669201660910.....
  22.  
  23. Another way of deriving the number is to use the bifurcation fractal. If
  24. you start fractint, hit 't' and choose bifurcation, a picture appears.
  25. It consists of a single line coming in from the left, which soon splits
  26. into two, and then four, and so on. The ratio of the distances between
  27. sucsessive splits (bifurcations) is Feigenbaum's number. 
  28.  
  29. I got the number and description out of "The Beauty of Fractals" by
  30. Peitgen and Richter.
  31.  
  32. I met Mitch Feigenbaum at the Nobel Conference in Minnesota in 1991. He
  33. was an animated, interesting man, who told hilarious stories at dinner.
  34. Mitch, if you read this newsgroup, I really enjoyed our conversation!
  35.  
  36. - --------------------------------------------------------------
  37. Thanks for using Fractint, The Fractals and Fractint Discussion List
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  42.  
  43. ------------------------------
  44.  
  45. Date: Thu, 05 Aug 1999 18:39:58 -0600
  46. From: Phil McRevis <legalize@xmission.com>
  47. Subject: Re: (fractint) Feigenbaum's Number 
  48.  
  49. In article <37AA1176.ECE3A2B4@mn.mediaone.net>,
  50.     David Kosokar <dkosokar@mn.mediaone.net>  writes:
  51.  
  52. > Feigenbaum's number = 4.669201660910.....
  53. > 
  54. > Another way of deriving the number is to use the bifurcation fractal.
  55.  
  56. The dynamics of the bifurcation fractal are *exactly* the dynamics of
  57. the Mandelbrot set on the real line.  A friend of mine once wrote a
  58. nice fractal demo program that plotted the bifurcation fractal dynamics
  59. over the M-set image and it was blatantly obvious.  Every place where
  60. the bifurcation fractal coalesces into a collection of points
  61. vertically stacke on top of each other is *exactly* the spot on the
  62. M-set images where the buds pinch out to a single point.  Its quite
  63. cool to see both properly superimposed because it elevates your
  64. understanding of both those fractal types.
  65. - --
  66. <http://www.xmission.com/~legalize/>    Legalize Adulthood!
  67.     ``Ain't it funny that they all fire the pistol,     
  68.       at the wrong end of the race?''--PDBT     
  69. legalize@xmission.com    <http://www.thewho.net>
  70.  
  71. - --------------------------------------------------------------
  72. Thanks for using Fractint, The Fractals and Fractint Discussion List
  73. Post Message:   fractint@lists.xmission.com
  74. Get Commands:   majordomo@lists.xmission.com "help"
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  77.  
  78. ------------------------------
  79.  
  80. Date: Fri, 6 Aug 1999 19:25:47 -0700
  81. From: "Jay Hill" <ehill1@san.rr.com>
  82. Subject: Re: (fractint) Feigenbaum's Number 
  83.  
  84. Feigenbaum's numbers have been computer to hundreds of digits by K. Briggs.
  85.  
  86. http://www-epidem.plantsci.cam.ac.uk/~kbriggs/pubs.html
  87.  
  88. see also http://www.mathsoft.com/asolve/constant/fgnbaum/brdhrst.html
  89.  
  90. Jay
  91.  
  92.  
  93. - --------------------------------------------------------------
  94. Thanks for using Fractint, The Fractals and Fractint Discussion List
  95. Post Message:   fractint@lists.xmission.com
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  99.  
  100. ------------------------------
  101.  
  102. Date: Sun, 08 Aug 1999 00:34:11 GMT
  103. From: karen_mc@mindspring.com (karen)
  104. Subject: (fractint) Herman rings?
  105.  
  106. I'm looking for the following two Fractint files and the names of the
  107. authors: 
  108.  
  109.           hring.frm
  110.           hringgal.par
  111.  
  112. Does anyone have a copy of these or know where they can be downloaded?
  113. Thanks in advance.
  114.  
  115.  
  116. karen
  117.  
  118. - --------------------------------------------------------------
  119. Thanks for using Fractint, The Fractals and Fractint Discussion List
  120. Post Message:   fractint@lists.xmission.com
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  122. Administrator:  twegner@phoenix.net
  123. Unsubscribe:    majordomo@lists.xmission.com "unsubscribe fractint"
  124.  
  125. ------------------------------
  126.  
  127. Date: Sat, 07 Aug 1999 20:21:27 -0700
  128. From: Ken Childress <icent@best.com>
  129. Subject: Re: (fractint) Herman rings?
  130.  
  131. - --=====================_188738==_
  132. Content-Type: text/plain; charset="us-ascii"
  133.  
  134.  
  135. Karen,
  136.  
  137. >I'm looking for the following two Fractint files and the names of the
  138. >authors: 
  139. >
  140. >          hring.frm
  141. >          hringgal.par
  142. >
  143. >Does anyone have a copy of these or know where they can be downloaded?
  144. >Thanks in advance.
  145.  
  146. I found them in a directory for Paul Derbyshire.  I don't remember
  147. where I downloaded them.
  148.  
  149. Here you go...
  150.  
  151.  
  152. Ken...
  153.  
  154. - ----------------------------
  155.  
  156.  
  157. - --=====================_188738==_
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  493. - --=====================_188738==_--
  494.  
  495.  
  496. - --------------------------------------------------------------
  497. Thanks for using Fractint, The Fractals and Fractint Discussion List
  498. Post Message:   fractint@lists.xmission.com
  499. Get Commands:   majordomo@lists.xmission.com "help"
  500. Administrator:  twegner@phoenix.net
  501. Unsubscribe:    majordomo@lists.xmission.com "unsubscribe fractint"
  502.  
  503. ------------------------------
  504.  
  505. Date: Sun, 08 Aug 1999 12:20:27 -0500
  506. From: "Paul N. Lee" <Paul.N.Lee@Worldnet.att.net>
  507. Subject: Re: (fractint) Herman rings?
  508.  
  509. Karen wrote:
  510. > 
  511. > I'm looking for the following two Fractint files and
  512. > the names of the authors:
  513. > 
  514. >           hring.frm
  515. >           hringgal.par
  516. > 
  517. > Does anyone have a copy of these or know where they
  518. > can be downloaded?   Thanks in advance.
  519. >
  520.  
  521. Most of the information regarding these two items, and several more
  522. PARs, may be found in the FractInt Archives (see postings starting
  523. around May 19, 1999) when Paul Derbyshire sent a bunch of new fractals:
  524.  
  525.     ftp://ftp.xmission.com/pub/lists/fractint/
  526.  
  527.  
  528. I believe Paul posted the actual formula way back in January of 1998:
  529.  
  530. - --8<-- hring.frm -->8--
  531.  
  532. HRing_J { ; This thing is capable of generating Herman rings for alpha
  533.           ; equal to exp(2*pi*i*a), a irrational.
  534.           ; p1: alpha. p2: c. p3: Orbit trap radius about 0, reciprocal
  535. is
  536.           ; used for infinity.
  537.           ; Use outside=real, logmap=0, periodicity=0.
  538.   z=pixel, a=p1, c=p2, r=real(p3), rr=1/r, iter=0, done=0:
  539.   z2=sqr(z)
  540.   z=a*z2*(z-c)/(1-c*z)
  541.   iter=iter+1
  542.   IF(lastsqr<r || lastsqr>rr)
  543.     color=iter
  544.     IF(color<1)
  545.       color=1
  546.     ELSEIF(color>127)
  547.       color=127
  548.     ENDIF
  549.     IF(lastsqr<r)
  550.       color=color+127
  551.     ENDIF
  552.     z=color-iter-7
  553.     done=1
  554.   ENDIF
  555.   done==0
  556. }
  557.  
  558. HRing_J2 { ; This thing is capable of generating Herman rings for alpha
  559.            ; equal to exp(2*pi*i*a), a irrational.
  560.            ; p1: alpha. p2: c. p3: Orbit trap radius about 0, reciprocal
  561. is
  562.            ; used for infinity.
  563.            ; Color variant: stretches to maxiter.
  564.            ; Use outside=real, logmap=0, periodicity=0.
  565.   z=pixel, a=p1, c=p2, r=real(p3), rr=1/r, iter=0, done=0:
  566.   z2=sqr(z)
  567.   z=a*z2*(z-c)/(1-c*z)
  568.   iter=iter+1
  569.   IF(lastsqr<r || lastsqr>rr)
  570.     color=(iter/maxit)*127
  571.     IF(color<1)
  572.       color=1
  573.     ELSEIF(color>127)
  574.       color=127
  575.     ENDIF
  576.     IF(lastsqr<r)
  577.       color=color+127
  578.     ENDIF
  579.     z=color-iter-7
  580.     done=1
  581.   ENDIF
  582.   done==0
  583. }
  584.  
  585. HRing_Mc { ; Mandelbrot set slice, c varies, alpha fixed.
  586.            ; p1: alpha. p3: Orbit trap radius about 0, reciprocal is
  587.            ; used for infinity.
  588.            ; Use outside=real, logmap=0, periodicity=0.
  589.   a=p1, c=pixel, r=real(p3), rr=1/r, iter=0, done=0, flag=0, m=maxit
  590.   z=(3+sqr(c)+sqrt(9-10*sqr(c)+sqr(sqr(c))))/(4*c)
  591.   IF(real(c)*real(c)-imag(c)*imag(c)-5>=0)
  592.     flag=1-flag
  593.   ENDIF
  594.   IF(imag(c)<0)
  595.     flag=1-flag
  596.   ENDIF
  597.   IF(flag==1)
  598.     z=(3+sqr(c)-sqrt(9-10*sqr(c)+sqr(sqr(c))))/(4*c)
  599.   ENDIF
  600.   :
  601.   z2=sqr(z)
  602.   z=a*z2*(z-c)/(1-c*z)
  603.   iter=iter+1
  604.   IF(lastsqr<r || lastsqr>rr)
  605.     color=(iter/maxit)*127
  606.     IF(color<1)
  607.       color=1
  608.     ELSEIF(color>127)
  609.       color=127
  610.     ENDIF
  611.     IF(lastsqr<r)
  612.       color=color+127
  613.     ENDIF
  614.     z=color-iter-7
  615.     done=1
  616.   ENDIF
  617.   done==0
  618. }
  619.  
  620. HRing_Ma { ; Mandelbrot set slice, alpha varies, c fixed.
  621.            ; p2: c. p3: Orbit trap radius about 0, reciprocal is
  622.            ; used for infinity.
  623.            ; Use outside=real, logmap=0, periodicity=0.
  624.   a=pixel, c=p2, r=real(p3), rr=1/r, iter=0, done=0, flag=0, m=maxit
  625.   z=(3+sqr(c)+sqrt(9-10*sqr(c)+sqr(sqr(c))))/(4*c)
  626.   IF(real(c)*real(c)-imag(c)*imag(c)-5>=0)
  627.     flag=1-flag
  628.   ENDIF
  629.   IF(imag(c)<0)
  630.     flag=1-flag
  631.   ENDIF
  632.   IF(flag==1)
  633.     z=(3+sqr(c)-sqrt(9-10*sqr(c)+sqr(sqr(c))))/(4*c)
  634.   ENDIF
  635.   :
  636.   z2=sqr(z)
  637.   z=a*z2*(z-c)/(1-c*z)
  638.   iter=iter+1
  639.   IF(lastsqr<r || lastsqr>rr)
  640.     color=(iter/maxit)*127
  641.     IF(color<1)
  642.       color=1
  643.     ELSEIF(color>127)
  644.       color=127
  645.     ENDIF
  646.     IF(lastsqr<r)
  647.       color=color+127
  648.     ENDIF
  649.     z=color-iter-7
  650.     done=1
  651.   ENDIF
  652.   done==0
  653. }
  654.  
  655. - ---8<--- hring.par --->8---
  656.  
  657.  
  658.  
  659.  
  660. P.N.L.
  661. - --------------------------------------------------------------
  662. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go
  663.  
  664. - --------------------------------------------------------------
  665. Thanks for using Fractint, The Fractals and Fractint Discussion List
  666. Post Message:   fractint@lists.xmission.com
  667. Get Commands:   majordomo@lists.xmission.com "help"
  668. Administrator:  twegner@phoenix.net
  669. Unsubscribe:    majordomo@lists.xmission.com "unsubscribe fractint"
  670.  
  671. ------------------------------
  672.  
  673. Date: Tue, 10 Aug 1999 20:00:25 -0400
  674. From: JoWeber <JoWeber@compuserve.com>
  675. Subject: (fractint) The little dragon pars
  676.  
  677. Hi All,
  678.  
  679. see the little dragon.
  680.  
  681. Enjoy --Jo--
  682.  
  683. http://www.jochenweber.de
  684.  
  685. 6m270700           { ; t=3D  0:15:54.11 =
  686.  
  687.                      ; on a P233MMX at 1600x1200  Aug 11, 1999  01:53:14
  688.                      ; Par and Image Copyright 1999 by Jo Weber
  689.                      ; e-mail to JoWeber@compuserve.com
  690.   reset=3D1960 type=3Dformula formulafile=3Dfractint.frm
  691.   formulaname=3Dmandnewt06 passes=3D1
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  710.   bh8
  711.   }
  712.  
  713. 6m270703           { ; t=3D  0:08:21.24 =
  714.  
  715.                      ; on a P233MMX at 1600x1200  Aug 11, 1999  01:53:43
  716.                      ; Par and Image Copyright 1999 by Jo Weber
  717.                      ; e-mail to JoWeber@compuserve.com
  718.   reset=3D1960 type=3Dformula formulafile=3Dfractint.frm
  719.   formulaname=3Dmandnewt06 passes=3Dt
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  736.   <2>45C569335000000400<2>A00C00C00D00000F00<9>O00<4>zg0<3>oU007A<2>0FM<7=
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  738.   bh8
  739.   }
  740.  
  741. 6m270708           { ; t=3D  0:07:45.66 =
  742.  
  743.                      ; on a P233MMX at 1600x1200  Aug 11, 1999  01:53:53
  744.                      ; Par and Image Copyright 1999 by Jo Weber
  745.                      ; e-mail to JoWeber@compuserve.com
  746.   reset=3D1960 type=3Dformula formulafile=3Dfractint.frm
  747.   formulaname=3Dmandnewt06 passes=3Dt
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  751.   463911863/0.5167440397350994/2.771819284646138 float=3Dy maxiter=3D100
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  766.   bh8
  767.   }
  768.  
  769. 6m270709           { ; t=3D  0:05:25.32 =
  770.  
  771.                      ; on a P233MMX at 1600x1200  Aug 11, 1999  01:54:08
  772.                      ; Par and Image Copyright 1999 by Jo Weber
  773.                      ; e-mail to JoWeber@compuserve.com
  774.   reset=3D1960 type=3Dformula formulafile=3Dfractint.frm
  775.   formulaname=3Dmandnewt06 passes=3Dt
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  779.   397930845/0.5654553956724754/2.837827005829035 float=3Dy maxiter=3D100
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  788.   Wg<2>Xcr<14>23300000500A<5>08E<7>NW5Q_3Tb2We0Tb1<7>9E96AB47A149000<3>II=
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  792.   <2>45C569335000000400<2>A00C00C00D00000F00<9>O00<4>zg0<3>oU007A<2>0FM<7=
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  794.   bh8
  795.   }
  796.  
  797. 6m270714           { ; t=3D  0:06:16.07 =
  798.  
  799.                      ; on a P233MMX at 1600x1200  Aug 11, 1999  01:54:17
  800.                      ; Par and Image Copyright 1999 by Jo Weber
  801.                      ; e-mail to JoWeber@compuserve.com
  802.   reset=3D1960 type=3Dformula formulafile=3Dfractint.frm
  803.   formulaname=3Dmandnewt06 passes=3Dt
  804.   center-mag=3D0.315568/-0.582894/0.4807146/1/-130
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  806. 727\
  807.   8337961974/0.5233093340861232/2.538959242530595 float=3Dy maxiter=3D100=
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  809.   bailout=3D25 inside=3Dbof60 logmap=3Dyes symmetry=3Dnone periodicity=3D=
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  815.   2>p80<2>R00P00<4>000023057<2>046045144143142132131220457<5>HKSJNWMQ_OTc=
  816. Q\
  817.   Wg<2>Xcr<14>23300000500A<5>08E<7>NW5Q_3Tb2We0Tb1<7>9E96AB47A149000<3>II=
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  820. L\
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  823.   bh8
  824.   }
  825.  
  826. 6m270720           { ; t=3D  0:06:38.87 =
  827.  
  828.                      ; on a P233MMX at 1600x1200  Aug 11, 1999  01:54:27
  829.                      ; Par and Image Copyright 1999 by Jo Weber
  830.                      ; e-mail to JoWeber@compuserve.com
  831.   reset=3D1960 type=3Dformula formulafile=3Dfractint.frm
  832.   formulaname=3Dmandnewt06 passes=3Dt
  833.   center-mag=3D0.180189/-0.392351/0.9228867/1/-130
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  836.   442335276/0.3328280571916868/2.89886402478103 float=3Dy maxiter=3D100
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  851.   bh8
  852.   }
  853.  
  854. 6m270723           { ; t=3D  0:07:20.45 =
  855.  
  856.                      ; on a P233MMX at 1600x1200  Aug 11, 1999  01:54:39
  857.                      ; Par and Image Copyright 1999 by Jo Weber
  858.                      ; e-mail to JoWeber@compuserve.com
  859.   reset=3D1960 type=3Dformula formulafile=3Dfractint.frm
  860.   formulaname=3Dmandnewt06 passes=3Dt
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  864.   590838343/0.4401921735282449/2.745813699758904 float=3Dy maxiter=3D100
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  869.   7TG7UC5M83F42763A00G022<6>0MM0P00M24L08TW<2>KWcOXeSYgWZi_XZ<2>lQ0iN0gJ0=
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  879.   bh8
  880.   }
  881.  
  882. 6m270733           { ; t=3D  0:07:07.10 =
  883.  
  884.                      ; on a P233MMX at 1600x1200  Aug 11, 1999  01:54:49
  885.                      ; Par and Image Copyright 1999 by Jo Weber
  886.                      ; e-mail to JoWeber@compuserve.com
  887.   reset=3D1960 type=3Dformula formulafile=3Dfractint.frm
  888.   formulaname=3Dmandnewt06 passes=3Dt
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  906.   <2>45C569335000000400<2>A00C00C00D00000F00<9>O00<4>zg0<3>oU007A<2>0FM<7=
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  908.   bh8
  909.   }
  910.  
  911. 6m270738           { ; t=3D  0:06:51.83 =
  912.  
  913.                      ; on a P233MMX at 1600x1200  Aug 11, 1999  01:55:01
  914.                      ; Par and Image Copyright 1999 by Jo Weber
  915.                      ; e-mail to JoWeber@compuserve.com
  916.   reset=3D1960 type=3Dformula formulafile=3Dfractint.frm
  917.   formulaname=3Dmandnewt06 passes=3Dt
  918.   center-mag=3D0.252958/-0.491065/0.8132693/1/-130
  919.   params=3D0.06889390240180671/-2.3850571642201/0.888291784417249/1.59654=
  920. 146\
  921.   8550676/0.4737129413739433/2.703381527146214 float=3Dy maxiter=3D100
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  924.   colors=3D000r_FtaDvdByg8yh5yi3yg3<2>ga3<33>301<11>b0Ee0Ff5I<10>zzs<7>fV=
  925. 7cQ\
  926.   0`O0<2>SI0<6>P60<2>G00<4>0Qc<6>8bcAdcDed<11>tupxwrzyt<7>ylDxj2wiK<3>vc4=
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  931.   }
  932.  
  933. frm:MandNewt06 {; Jim Muth
  934. z=3Dc=3D(pixel*p1):
  935. a=3Dz^3+(c-p2)*z-c
  936. b=3Dp3*z^2+c-1
  937. z=3Dz-1*a/b
  938. .000000000000000000000000000001 <=3D |a|
  939. }
  940.  
  941.  
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  949. ------------------------------
  950.  
  951. End of fractint-digest V1 #404
  952. ******************************
  953.  
  954.