Date: Sat, 10 Jan 1998 06:42:51 -0500 (EST)
Message-Id: <199801101142.GAA06209@freenet5.carleton.ca.carleton.ca>
From: ao950@freenet.carleton.ca (Paul Derbyshire)
To: fractint@lists.xmission.com
Subject: Re: (fractint) Liouville Julia set
Sender: owner-fractint@lists.xmission.com
Precedence: bulk
Reply-To: fractint@lists.xmission.com
Content-Type: text

>Hi Paul,
>
>>The Liouville one is fascinating to study using the orbits window. 
>> Generate it and hit o, and look at the assorted orbits for points 
>> in the interior. 
>
>Very interesting. The orbit on a P200 gave the impression of a beating heart.
>
>I reproduce your par here with slight zoom in and color change so 
>I can see the edge a little better. I also toss out two others...these are 
>really chunky fractals! If we use passes=g we don't see correct valleys.

What the hell internal angles did you use for those two? I don't myself
know of any other Liouville numbers.
As for passes=g, I had noticed. :P It sure is slow with maxit=1048576 and
passes=1...took me a whole 2 minutes. Yeachk. Fascinating end results though.

>> namely that the brain contains structures that operate as quantum 
>> computers not subject to the limitations of classical mechanics, nor 
>> to the Turing machine's limits of finite states and finite speed. 
>
>I have the other day teased one of the computer science types I know
>about the stopping problem applied to the brain. I suggested it might be 
>fear of such that drives some at the office to drink so much coffee!  
>(Would not want that up stairs computer to stop while contemplating 
>one of your Siegel disks.)  On the other hand,  I pointed out to him that 
>quantum effects might allow the brain to restart.  

There're plenty more Siegel disks... just check my post outlining an
algorithm for identifying a representative point for each finite attractor
and the center and a characteristic of each Siegel disk in an arbitrary
Julia set image of any kind, and detect convergence to any of the above
for each image pixel.

>I agree. A few years ago I posted to sci.fractals an article titled
>The Mandelbrot Chaosometer where I describe some aspects 
>of this problem.

All of a sudden, I want to fiddle around with Lyapunov exponents...Julia
coloring by Lyapunov exponents, Mandelbrot by that of the critical
point... I wonder why...

Say I wonder what the Lyapunov exponent does in a Siegel disk? Stays near
zero perhaps?

>Jay
>
>Liouville-1    { ; Paul Derbyshire
>                 ; zoom in and color change by Jay Hill
>  reset=1960 type=lambda passes=1
>  center-mag=0.5/4.44089e-016/0.8912656
>  params=0.09801751303322832/-0.9951846899640191 float=y
>  maxiter=1048576 inside=0 logmap=yes
>  colors=000F0K<29>i0xk0zj0z<29>20z01z01z<30>0Uz1Vz3Wz<28>xxzzzzzzx<59>zz1\
>  zz0zy0yx0<56>I4IH3JG2JF0KF0KF0KF0K
>  savename=Liouvill
>  }
>
>Siegel-1       { ; Paul Derbyshire
>                 ; zoom in and color change by Jay Hill
>                 ; params=exp(2*i*pi*a), a=(sqrt(5.)-1.)/2.
>  reset=1960 type=lambda center-mag=0.5/6.66134e-016/0.9861933
>  params=-0.7373688780783196/-0.675490294261524 float=y
>  maxiter=1048576 inside=0 logmap=yes passes=1
>  colors=000F0K<29>i0xk0zj0z<29>20z01z01z<30>0Uz1Vz3Wz<28>xxzzzzzzx<59>zz1\
>  zz0zy0yx0<56>I4IH3JG2JF0KF0KF0KF0K
>  savename=Siegel
>  }
>
>Siegel-2 { ; Jay Hill  
>           ; params=exp(2*i*pi*a), a=(sqrt(3.)-1.)/2.
>  reset=1960 type=lambda center-mag=0.5/6.66134e-016/0.9861933
>  params=-0.666130923602528/0.745834829315743 float=y
>  maxiter=1048576 inside=0 logmap=yes passes=1
>  colors=000F0K<29>i0xk0zj0z<29>20z01z01z<30>0Uz1Vz3Wz<28>xxzzzzzzx<59>zz1\
>  zz0zy0yx0<56>I4IH3JG2JF0KF0KF0KF0K
>  savename=Siegel2
>  }
>
>Siegel-3 { ; Jay Hill   
>           ; params=exp(2*i*pi*a), a=(sqrt(7.)-1.)/2.
>  reset=1960 type=lambda center-mag=0.5/6.66134e-016/0.9861933
>  params=0.442057568870217/-0.896986680951592 float=y
>  maxiter=1048576 inside=0 logmap=yes passes=1
>  colors=000F0K<29>i0xk0zj0z<29>20z01z01z<30>0Uz1Vz3Wz<28>xxzzzzzzx<59>zz1\
>  zz0zy0yx0<56>I4IH3JG2JF0KF0KF0KF0K
>  savename=Siegel3
>  }

Arg. Not two new Liouvilles, two Siegels. :-)

Algebraic Siegels look a bit different from transcendental ones sometimes.
(Transcendental as in, pi-3, pi/4, e-2, e/3, 1/pi, 1/sqrt(pi), etc... Heck
even try (pi+e-5)^2.7! or exp(e-2)... gak. Inventing freaky transcendental
numbers rapidly produces prolific irrationals in prodigious quantities
with no practical value whatsoever. :-))

I gotta say, you definitely know your math, not just complex and
exponential, but even the Mandelmath from TBOF. :-)

--
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire ao950@freenet.carleton.ca pgd73@hotmail.com

-
------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   fractint@xmission.com
Get Commands:   majordomo@xmission.com "help"
Administrator:  twegner@phoenix.net
Unsubscribe:    majordomo@xmission.com "unsubscribe fractint"