In article <1294003306.3956.1.camel@jonathan-desktop>,

   Jonathan Osuch <osuchj@avalon.net> writes:

> Tony,
>
> > I'm looking for the order number translation for the string
> > bbbbbbaaaaaa to use in Fractint, which produces this Lyapunov fractal:
> > http://commons.wikimedia.org/wiki/File:Lyapunov-fractal.png
> > (It's a famous one, called Zircon City.)
> > Any help?
>
> Try this:
>
> ZirconCity         {
>   reset=2004 type=lyapunov passes=1 corners=2.5/3.4/3.4/4
>   params=992/0.5/0 float=y maxiter=500 inside=0
>   colors=000zk0<189>G10G10F00<61>000
>   }

By my calculations it should be 4032 instead of 992.  Am I wrong?

See attached perl script I used to translate back and forth.
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#!/usr/local/bin/perl -w

sub AlphaToOrderInteger($)
{
       my($alpha) = @_;
       if ($alpha !~ /b/)
       {
               print "Alpha '$alpha' must contain at least one 'b'\n";
               return 1;
       }
       while ($alpha =~ /^a/)
       {
               $alpha = substr($alpha, 1) . substr($alpha, 0, 1);
       }
       my($order) = 1;
       $alpha = substr($alpha, 1);
       while (length($alpha) > 0)
       {
               $order <<= 1;
               my($ab) = substr($alpha, 0, 1);
               $alpha = substr($alpha, 1);
               if ($ab eq 'b')
               {
                       $order |= 1;
               }
       }
       print "Order: $order\n";

       return 0;
}

sub OrderIntegerToAlpha($)
{
       my($order) = @_;
       my($alpha) = '';
       while ($order > 0)
       {
               $alpha = (($order & 1) ? 'b' : 'a') . $alpha;
               $order >>= 1;
       }
       print "Alpha: $alpha\n";

       return 0;
}

sub main()
{
       if ($#ARGV != 0)
       {
               print "Usage: lyapunov-order.pl order\n";
               return 1;
       }

       my($arg) = $ARGV[0];
       if ($arg =~ /a/i)
       {
               return AlphaToOrderInteger($arg);
       }
       return OrderIntegerToAlpha($arg);
}

exit(main());

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