March 2002 - Fractint - mailman.xmission.com

Something interesting
by Multiple Bogeys 23 Mar '02

23 Mar '02

This might be intriguing. An endless variety of Siegel disks can be constructed using the polynomials z^n + cz, n > 1 here cz determines a rotation; c = exp(2*pi*i*a) with a irrational on [0,1] gives Siegel disks. 0 is a fixed point (obviously) and the derivative at 0 is c. Just z -> cz rotates the whole plane by the angle a, but adding the "nonlinear seed" z^n crinkles the invariant circles and creates a superattractor at infinity. Siegel disks are the result. I got this from some web research on siegel disks I did recently. Now consider this: z^n + (az+b)/(cz+d), n > 1 We've replaced the rotation with a semilinear transformation. If ad-bc is nonzero, it combines a scaling, a rotation, and possibly inversion in the unit circle. If |ad-bc| = 1, there's no scaling involved. If |ad-bc| is exp(2*pi*i*x) with x irrational, the result should be Siegel-like in quality, with the unit circle distorted and crinkled into an invariant curve. However, the fate of 0 in this map is different. It's a fixed point if d != 0, but the derivative there is (ad-bc)/(d^2), so if d is large, 0 is quite strongly *attracting* rather than indifferent. Our siegel disk might well have a *hole* in it. OTOH, if d is 0, neither b nor c are 0 (we have assumed ad-bc != 0 remember) and so zero goes to 0^n + b/0, i.e. is a preimage of the superattracting fixed point at infinity. Again we have a "hole"... Something strange might be possible. Perhaps I'll investigate using fractint...Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

1 0

Re: [Fractint] FOTD 18-03-02 (Fractal DuJour [6])
by Multiple Bogeys 23 Mar '02

23 Mar '02

This one is incredibly beautiful Shoulda rated it a 9 :)Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

1 0

FOTD 21-03-02 (Octagonal Chaos [6])
by JimMuth＠aol.com 21 Mar '02

21 Mar '02

FOTD -- March 21, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows a midget very near the northeast shoreline of the main bay of the M-set. The midget lies so close to the area of trapped points that the pattern around it is well on the way to degenerating into a featureless chaos. The pattern is still quite recognizable however, and makes a picture worth a 6 on my subjective scale of fractal value. I named the image "Octagonal Chaos" after the prominent octagon surrounding the midget. Perhaps the name is a bit presumptive, for the octagon is totally an artifact of the coloring, and does not exist in the actual underlying shapes. As with all type=mandel images, this one is a quickie, rendering in a zippy 2 minutes -- about equal to the time it would take to download the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Wednesday featured steady rain most of the day and temperatures in the 40's F, or around 7C. Even when the rain ended, the grass was too wet for the cats to walk in. As a result, the dynamic duo were sulky, and needed an extra tuna treat. I'm also a bit sulky, with lots of regular work to do and in addition the work on the FOTD-CD, which seems to be turning into a larger job every time I tackle it. Regardless however, I'll return on the 24th with the next FOTD, which, if all goes as planned, will be an image of a midget drowning in chaos. Until then, take care, and do not fret -- the FOTD will resume its daily schedule as soon as the CD is ready for distribution. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Octagonal_Chaos { ; time=0:02:36.86--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=+0.2970\ 2042485981/+0.44815266222845/2.524655e+009/1/-120/\ 4.1133437767779113e-006 params=0/0 float=y maxiter=16000 inside=0 logmap=-2932 colors=00000M01L02K03J04I05H06G07F08E09D1AC2BB3CA4\ D95E800600800900B00C00E00F00H00J00L00N00P00R00TKzK\ NzOPzSRzVUwZWtbZqf`nibkmehqgeuibxe_wbXv_UtXRrUOpRL\ oNImKFkHCiE9gB7e85d98cABbBEaBG`CJ_FM_KPZPRYUUXZXWc\ _UhaTmWPrQLrKHlEDfIF`MGZPIcTJgXKf_MecNefO2j27d6C_9\ GVDLQGPKKUFNYARb5Uf0Xb8VZGUVOTSWROcQKmPHwOLzPOzPSr\ PVmPZhPacPeZPhUPlPPoKPsFPvAPy5Pv7RsASpDUnFVkIWhLYe\ OZcQ_`TaYWbVZdT`eQcfNfhKiiIkjHghGcgG_fFWdEScEPbDL`\ CH_CDZB9XA5WA2VC5XE8YFAZHD_IF`KIaLKbNNcOPdQSeRUfTX\ gUZhXW`_UUaSNXWLT_KPcILfHOhGQiGSkGUlGWmFYoF_pFbqFd\ sFftEhuEjwElxEnyEmsIlmLlmOkmSjmVjmYimahmdhmgem`bmU\ _mNXmGUm9VmAWmAXmAYmAZmB_mB_mB`mBamCbmCcmCdmCdnCZo\ 9Tp7Nq5Hr3Bs1Et7HuCKvHNwMQxSTyXWzaYzf`zhczjDzXBzRO\ z``zjYzgVzdSzbQz_NzXKzVHzSFzPCzN9zK7zIEzOKzTQzZXzc\ bzihznnzsmzrlzqkzpjzojzoiznhzmgzlfzkfzkezjdziczhbz\ gbzgVzmNzrFzwLzsRzpTzkVzg } END PARAMETER FILE=========================================

1 0

FOTD 21-03-02 (Octagonal Chaos [6])
by JimMuth＠aol.com 21 Mar '02

21 Mar '02

FOTD -- March 21, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows a midget very near the northeast shoreline of the main bay of the M-set. The midget lies so close to the area of trapped points that the pattern around it is well on the way to degenerating into a featureless chaos. The pattern is still quite recognizable however, and makes a picture worth a 6 on my subjective scale of fractal value. I named the image "Octagonal Chaos" after the prominent octagon surrounding the midget. Perhaps the name is a bit presumptive, for the octagon is totally an artifact of the coloring, and does not exist in the actual underlying shapes. As with all type=mandel images, this one is a quickie, rendering in a zippy 2 minutes -- about equal to the time it would take to download the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Wednesday featured steady rain most of the day and temperatures in the 40's F, or around 7C. Even when the rain ended, the grass was too wet for the cats to walk in. As a result, the dynamic duo were sulky, and needed an extra tuna treat. I'm also a bit sulky, with lots of regular work to do and in addition the work on the FOTD-CD, which seems to be turning into a larger job every time I tackle it. Regardless however, I'll return on the 24th with the next FOTD, which, if all goes as planned, will be an image of a midget drowning in chaos. Until then, take care, and do not fret -- the FOTD will resume its daily schedule as soon as the CD is ready for distribution. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Octagonal_Chaos { ; time=0:02:36.86--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=+0.2970\ 2042485981/+0.44815266222845/2.524655e+009/1/-120/\ 4.1133437767779113e-006 params=0/0 float=y maxiter=16000 inside=0 logmap=-2932 colors=00000M01L02K03J04I05H06G07F08E09D1AC2BB3CA4\ D95E800600800900B00C00E00F00H00J00L00N00P00R00TKzK\ NzOPzSRzVUwZWtbZqf`nibkmehqgeuibxe_wbXv_UtXRrUOpRL\ oNImKFkHCiE9gB7e85d98cABbBEaBG`CJ_FM_KPZPRYUUXZXWc\ _UhaTmWPrQLrKHlEDfIF`MGZPIcTJgXKf_MecNefO2j27d6C_9\ GVDLQGPKKUFNYARb5Uf0Xb8VZGUVOTSWROcQKmPHwOLzPOzPSr\ PVmPZhPacPeZPhUPlPPoKPsFPvAPy5Pv7RsASpDUnFVkIWhLYe\ OZcQ_`TaYWbVZdT`eQcfNfhKiiIkjHghGcgG_fFWdEScEPbDL`\ CH_CDZB9XA5WA2VC5XE8YFAZHD_IF`KIaLKbNNcOPdQSeRUfTX\ gUZhXW`_UUaSNXWLT_KPcILfHOhGQiGSkGUlGWmFYoF_pFbqFd\ sFftEhuEjwElxEnyEmsIlmLlmOkmSjmVjmYimahmdhmgem`bmU\ _mNXmGUm9VmAWmAXmAYmAZmB_mB_mB`mBamCbmCcmCdmCdnCZo\ 9Tp7Nq5Hr3Bs1Et7HuCKvHNwMQxSTyXWzaYzf`zhczjDzXBzRO\ z``zjYzgVzdSzbQz_NzXKzVHzSFzPCzN9zK7zIEzOKzTQzZXzc\ bzihznnzsmzrlzqkzpjzojzoiznhzmgzlfzkfzkezjdziczhbz\ gbzgVzmNzrFzwLzsRzpTzkVzg } END PARAMETER FILE=========================================

1 0

Multivalued logic investigations
by Antoliano Dávila 19 Mar '02

19 Mar '02

Estimable Sr Doctorow: We are two computer science students from University of Malaga (Spain). First, please excuse our poor english level. We are at fifth year of our studies, and this year we have a subject about advanced logic and we choose an investigation about "Multivalued logic & applications". We were searching information about this area in the web, and we have found a reference to yours investigation about Fuzzy Multivalued Logic Basis of Fractals and Chaos. We would be pleasant to know about your works, and other possible links at web from this applications. Finally, thank you very much for your time and please, answer us as soon as possible. Greetings Juan Jose Carmona Falder Antoliano Davila Infantes.

1 0

Re-install problem.
by John W. 19 Mar '02

19 Mar '02

After re-installing Fractint recently I ran into a problem. My SSTOO:LS file is thus: [fractint] TEMPDIR=C:\Temp\ WORKDIR=C:\Fractals\FractInt\Work\ ; BATCH=yes ; AUTOKEY=play|record AUTOKEYNAME=C:\Fractals\FractInt\KEY_s\auto.key ; MAKEDOC=Fractint.doc MAXHISTORY=20 MAP=C:\Fractals\FractInt\MAP_s\*.map RECORDCOLORS=comment ; auto|comment|yes SAVENAME=C:\Fractals\FractInt\GIF_s\fract001.gif OVERWRITE=no ; no|yes ; SAVETIME=nnn|-nnn ; GIF87a=yes ; DITHER=yes PARMFILE=C:\Fractals\FractInt\PAR_s\*.par FORMULAFILE=C:\Fractals\FractInt\FRM_s\*.frm LFILE=C:\Fractals\FractInt\L_s\*.l IFSFILE=C:\Fractals\FractInt\IFS_s\*.ifs ; FILENAME=[.suffix] ; ORBITSAVE=yes VIDEO=SF6 ;800x600@ 256 TEXTSAFE=save ; yes|no|bios|save I'm pretty sure that's how it was before the re-installation. However, when I try to search through F6 for a (say) ".l" file, or a *.gif, or anything but a *.par file, then in the "Select Parameter Set File" window I see something like: Template: C:\ FRACTALS\FRACTINT\IF_S\*.par. That *.par is in every sub-directory. So where am I going astray? Please? John W..

2 2

FOTD 18-03-02 (Fractal DuJour [6])
by JimMuth＠aol.com 18 Mar '02

18 Mar '02

FOTD -- March 18, 2002 (Rating 6) Fractal visionaries and enthusiasts: Even as the FOTD-CD progresses, the new fractals keep coming. Today's is a typical example of my present fractal discoveries, which to keep the exploration time to a minimum, are often confined to the high-speed Mandel formula. Today's fractal is lively. It fairly leaps off the screen and runs across the floor. If it were created with the M-Mix4 formula, I would have rated it a 7 or an 8. But since it is a scene in the classic Mandelbrot set, which has been explored virtually ad-infinitum, I could rate it no higher than a 6. The image, of course, as are most of my images, is one of a midget. Such mini M-sets are sometimes called atoms. Yes, I realize that there is far more to the world of fractals than these tiny M-sets, but I have specialized in the field of midgets. After all, as with the field of science, the days have long passed when one can know everything about every fractal phenomenon. Today's unusually intricate scene is located close to the shore line of the main bay, in the area just beyond the region where the features degenerate into near-total chaos. I have named the image "Fractal DuJour" for no good reason that I can give. A name such as "Brazen" might have been better, but the present name was the first to enter my half-asleep mind, and the present name will remain. Perhaps the best feature of the image is it's speed. The 14-second render time makes the usual trip to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or to: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> to download the file of the completed GIF image, almost redundant. The weather at Fractal Central was miserable Sunday, with a cold raw 36F 2C wind off the ocean and a mixture of rain and sleet that kept the cats confined to quarters all day. The dynamic duo were unusually good-natured considering their confinement, but we'll see how long they can maintain their good natures. The inclement weather is due to continue most of this week. I'm now going to write a short note to the philofractal list. I'll return on the 21st with an equinox fractal. Until then, take care, and see you soon. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Fractal_DuJour { ; time=0:00:15.05--SF5 on a P200 reset=2002 type=mandel center-mag=-0.5915294272697\ 452/+0.4592677947779074/2.607822e+012/1/-30.005679\ 6126170795/-0.033435127060671109 params=0/0 float=y maxiter=2400 inside=0 logmap=334 mathtolerance=/1 colors=000I00K00M00O00Q01S02U03W05Y06_08a29c5Ae8Cg\ ADiDFkGImJIoMJqQJsULuXLw_LxbMveMvhOvkOvnPvrPvuPxrM\ zpLznIzkGziFzhCzeAzd8zb6z`5zY2zX1zW0zS0zQ0zP0zM0zL\ 0zJ0zI0zJ0zJ0zJ0zL0xL0uL0rM1nM3kM6hO8eOAbOC_PFXPGU\ PJSPLXSM_WOdYPg`PkdQngSsiSvmUzpWzsWzmSzhQzdOz_MzWL\ zQIzMGzIFzDCz9Az58z16z05z02z01z00z03z06x0Au0Dr3Ip6\ LmAPkFShIXeM_dQd`UgYYkXbnUesSivPnzMrzLvzIzzGzzIzzJ\ vzJszLpzLmzMizMgzOdzO`zPYzPWzQQzSOxSLvUIuUFsWCsW9r\ X6pX3nY1mY0mX1iW2hU5gU6eS8dQAbQC`PF_OGYOIXPJWPLUQL\ SQMSQMQSOPSOOSPOUPMUQLUQJWSJWSIWUGXUFXWFXWDYXCYXAY\ YA_Y9__8__8bdJdhWewegwrhwzkwsmwkpPdrFWu5Ov0Gr0Ji1L\ d3MY6OS9PMCQGFSAIU5LWAOSFPQJQPPSOUUMYWLdXJhYIm_Gr`\ FpYInXLnWOmSQmQUkPXkO_iL`iJdhIghGigDmgCpeAse9u`DsY\ IrUMpQQpMWnJYmFbkCgk8ki5ph1sg0xg0ze0zd0zb0zb0z_0zX\ 0zU2zQ8zOCzLGzILzFQzCWz9_z6dz3iz1nz0sz0xz0zz0vz0rz\ 0mz0gz0bz0Yz0Uz0Oz1Jz2Fz3 } END PARAMETER FILE=========================================

1 0

Re: Fig Tree Fractal and entropy production
by Gavin Ritz 18 Mar '02

18 Mar '02

Hi Can anyone help me with this problem. I am trying to create an entropy production diagram from the fig tree fractal. the formula for delta S (entropy) = X{n+1}*(X{n+1})/X{n}*(1-X{n}). I derived this formula from the Xnext formula and substituted that into the delta S formula of (lamda)*(change in flow, which is the same as X{n+1}-X{n}). Entropic forces create new flows (lamda or parameter r in some books) can be viewed as an entropic force). What the program needs to do is take out the repetitive points say for lamda (or parameter r) =3.5, x equals 0.875, 0.825, 0.5011, 0.3828. I was wondering if this could be done easily, can anyone help. kindest gavin

1 0

A few interpolated L-systems
by Morgan L. Owens 17 Mar '02

17 Mar '02

An exhibition of one approach to interpolating between successive iterations of an L-system. Others are certainly possible (and, as illustrated by SquareTiling, desirable.) Morgan L. Owens "These are rather jerky, unilluminating animations [of iterations of the Hilbert curve] since the process is discrete - there are no possible intermediate frames." KochCurve{ Angle 6 Axiom f f=f-f++f-f } HeighwayDragon{ Angle 4 Axiom xf f= x=xf+yf y=xf-yf } SquareTiling { Angle 4 Axiom s s=sfsf+fsf+fsf+ff+ f=gg g=gg } Pentigree {;William McWorter's Pentigree Angle 10 Axiom f f=-f--f|-f++f--f--f+ } Sierpinskicarpet{ Angle 4 Axiom f f=f[-f+f+f]+f-f-f+f } Hilbert { ; Ken Philip, from The Science of Fractal Images axiom x x=-YF+XFX+FY- y=+XF-YFY-FX+ angle 4 } Peano1 { Angle 4 Axiom f-f-f-f f=f-f+f+f+f-f-f-f+f } Peano3 { axiom x x=XFYFX+F+YFXFY-F-XFYFX y=YFXFY-F-XFYFX+F+YFXFY angle 4 } Sierpinski1 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle 3 axiom F F=FXF X=+FXF-FXF-FXF+ } Curve4 { ; Adrian Mariano axiom yf x=YF+XF+Y y=XF-YF-X angle 6 } KochCurve10{ Angle 6 Axiom d l=/50 r=\50 d=d/10ld\10\10rrd/10ld } KochCurve15{ Angle 6 Axiom d l=/45 r=\45 d=d/15ld\15\15rrd/15ld } KochCurve20{ Angle 6 Axiom d l=/40 r=\40 d=d/20ld\20\20rrd/20ld } KochCurve30{ Angle 6 Axiom d l=/30 r=\30 d=d/30ld\30\30rrd/30ld } KochCurve45{ Angle 6 Axiom d l=/15 r=\15 d=d/45ld\45\45rrd/45ld } KochCurve60{ Angle 6 Axiom d l= r= d=d/60ld\60\60rrd/60ld } HeighwayDragon10{ Angle 4 Axiom xd d= l=/80 r=\80 x=xd\10ryd y=xd/10lyd } HeighwayDragon30{ Angle 4 Axiom xd d= l=/60 r=\60 x=xd\30ryd y=xd/30lyd } HeighwayDragon45{ Angle 4 Axiom xd d= l=/45 r=\45 x=xd\45ryd y=xd/45lyd } HeighwayDragon60{ Angle 4 Axiom xd d= l=/30 r=\30 x=xd\60ryd y=xd/60lyd } HeighwayDragon80{ Angle 4 Axiom xd d= l=/10 r=\10 x=xd\80ryd y=xd/80lyd } HeighwayDragon90{ Angle 4 Axiom xd d= l= r= x=xd\90ryd y=xd/90lyd } SquareTiling10 { Angle 4 Axiom s r=\80 s=sdsd\10rdsd\10rdsd\10rdd\10r d=mm m=mm } SquareTiling30 { Angle 4 Axiom s r=\60 s=sdsd\30rdsd\30rdsd\30rdd\30r d=mm m=mm } SquareTiling45 { Angle 4 Axiom s r=\45 s=sdsd\45rdsd\45rdsd\45rdd\45r d=mm m=mm } SquareTiling60 { Angle 4 Axiom s r=\30 s=sdsd\60rdsd\60rdsd\60rdd\60r d=mm m=mm } SquareTiling80 { Angle 4 Axiom s r=\10 s=sdsd\80rdsd\80rdsd\80rdd\80r d=mm m=mm } SquareTiling81 { Angle 4 Axiom s r=/81\90 s=sdsd\81rdsd\81rdsd\81rdd\81r d=mm m=mm } SquareTiling82 { Angle 4 Axiom s r=/82\90 s=sdsd\82rdsd\82rdsd\82rdd\82r d=mm m=mm } SquareTiling83 { Angle 4 Axiom s r=/83\90 s=sdsd\83rdsd\83rdsd\83rdd\83r d=mm m=mm } SquareTiling84 { Angle 4 Axiom s r=/84\90 s=sdsd\84rdsd\84rdsd\84rdd\84r d=mm m=mm } SquareTiling85 { Angle 4 Axiom s r=/85\90 s=sdsd\85rdsd\85rdsd\85rdd\85r d=mm m=mm } SquareTiling86 { Angle 4 Axiom s r=/86\90 s=sdsd\86rdsd\86rdsd\86rdd\86r d=mm m=mm } SquareTiling87 { Angle 4 Axiom s r=/87\90 s=sdsd\87rdsd\87rdsd\87rdd\87r d=mm m=mm } SquareTiling88 { Angle 4 Axiom s r=/88\90 s=sdsd\88rdsd\88rdsd\88rdd\88r d=mm m=mm } SquareTiling89 { Angle 4 Axiom s r=\1 s=sdsd\89rdsd\89rdsd\89rdd\89r d=mm m=mm } SquareTiling90 { Angle 4 Axiom s r=/90\90 s=sdsd\90rdsd\90rdsd\90rdd\90r d=mm m=mm } Pentigree10 { Angle 10 Axiom d l=/26 r=\26 d=/10ld/10l/10ld\10r\10r\10r\10rd\10r\10rd/10l/10ld/10l/10ld\10r } Pentigree15 { Angle 10 Axiom d l=/21 r=\21 d=/15ld/15l/15ld\15r\15r\15r\15rd\15r\15rd/15l/15ld/15l/15ld\15r } Pentigree20 { Angle 10 Axiom d l=/16 r=\16 d=/20ld/20l/20ld\20r\20r\20r\20rd\20r\20rd/20l/20ld/20l/20ld\20r } Pentigree30 { Angle 10 Axiom d l=/6 r=\6 d=/30ld/30l/30ld\30r\30r\30r\30rd\30r\30rd/30l/30ld/30l/30ld\30r } Pentigree36 { Angle 10 Axiom d l= r= d=/36ld/36l/36ld\36r\36r\36r\36rd\36r\36rd/36l/36ld/36l/36ld\36r } Sierpinskicarpet10{ Angle 4 Axiom d l=/80 r=\80 d=d[/10ld\10rd\10rd]\10rd/10ld/10ld\10rd } Sierpinskicarpet15{ Angle 4 Axiom d l=/75 r=\75 d=d[/15ld\15rd\15rd]\15rd/15ld/15ld\15rd } Sierpinskicarpet30{ Angle 4 Axiom d l=/60 r=\60 d=d[/30ld\30rd\30rd]\30rd/30ld/30ld\30rd } Sierpinskicarpet45{ Angle 4 Axiom d l=/45 r=\45 d=d[/45ld\45rd\45rd]\45rd/45ld/45ld\45rd } Sierpinskicarpet60{ Angle 4 Axiom d l=/30 r=\30 d=d[/60ld\60rd\60rd]\60rd/60ld/60ld\60rd } Sierpinskicarpet80{ Angle 4 Axiom d l=/10 r=\10 d=d[/80ld\80rd\80rd]\80rd/80ld/80ld\80rd } Sierpinskicarpet90{ Angle 4 Axiom d l= r= d=d[/90ld\90rd\90rd]\90rd/90ld/90ld\90rd } Hilbert1 { axiom x l=\89 r=/89 x=/1lYd\1rXdX\1rdY/1l y=\1rXd/1lYdY/1ldX\1r angle 4 } Hilbert10 { axiom x l=\80 r=/80 x=/10lYd\10rXdX\10rdY/10l y=\10rXd/10lYdY/10ldX\10r angle 4 } Hilbert15 { axiom x l=\75 r=/75 x=/15lYd\15rXdX\15rdY/15l y=\15rXd/15lYdY/15ldX\15r angle 4 } Hilbert30 { axiom x l=\60 r=/60 x=/30lYd\30rXdX\30rdY/30l y=\30rXd/30lYdY/30ldX\30r angle 4 } Hilbert45 { axiom x l=\45 r=/45 x=/45lYd\45rXdX\45rdY/45l y=\45rXd/45lYdY/45ldX\45r angle 4 } Hilbert60 { axiom x l=\30 r=/30 x=/60lYd\60rXdX\60rdY/60l y=\60rXd/60lYdY/60ldX\60r angle 4 } Hilbert80 { axiom x l=\10 r=/10 x=/80lYd\80rXdX\80rdY/80l y=\80rXd/80lYdY/80ldX\80r angle 4 } Hilbert89 { axiom x l=\1 r=/1 x=/89lYd\89rXdX\89rdY/89l y=\89rXd/89lYdY/89ldX\89r angle 4 } Hilbert90 { axiom x l= r= x=/90lYd\90rXdX\90rdY/90l y=\90rXd/90lYdY/90ldX\90r angle 4 } Peano1-1 { Angle 4 Axiom d/90d/90d/90d l=/89 r=\89 d=d/1ld\1rd\1rd\1rd/1ld/1ld/1ld\1rd } Peano1-10 { Angle 4 Axiom d/90d/90d/90d l=/80 r=\80 d=d/10ld\10rd\10rd\10rd/10ld/10ld/10ld\10rd } Peano1-45 { Angle 4 Axiom d/90d/90d/90d l=/45 r=\45 d=d/45ld\45rd\45rd\45rd/45ld/45ld/45ld\45rd } Peano1-60 { Angle 4 Axiom d/90d/90d/90d l=/30 r=\30 d=d/60ld\60rd\60rd\60rd/60ld/60ld/60ld\60rd } Peano1-80 { Angle 4 Axiom d/90d/90d/90d l=/10 r=\10 d=d/80ld\80rd\80rd\80rd/80ld/80ld/80ld\80rd } Peano1-89 { Angle 4 l=/1 r=\1 Axiom d/90d/90d/90d d=d/89ld\89rd\89rd\89rd/89ld/89ld/89ld\89rd }

1 0

Makemap
by John W. 16 Mar '02

16 Mar '02

Anyone know of a working link to a copy of Ron Barnett's "Makemap"? Can't seem to find a copy any more! John W.

2 2