Thanks for this, Richard - I've seen the Help for Lyapunovs in FractInt, but still couldn't figure out how to get from my text string to an order number. Tony On 30 December 2010 10:33, Richard <legalize@xmission.com> wrote:

In article <AANLkTik2TWMhLxCmQAR7t8yWZsK3S8UEGU_cyRy13pvT@mail.gmail.com>, "Tony (Anthony) Hanmer" <a.hanmer@gmail.com> writes:

...

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?

I found this in a comment in the code. It should probably migrate to the help file for this fractal type:

The sequence is coded in the bit pattern in an integer. Briefly, the sequence starts with an A the leading zero bits are ignored and the remaining bit sequence is decoded. The sequence ends with a B. Not all possible sequences can be represented in this manner, but every possible sequence is either represented as itself, as a rotation of one of the representable sequences, or as the inverse of a representable sequence (swapping 0s and 1s in the array.) Sequences that are the rotation and/or inverses of another sequence will generate the same lyapunov exponents.

A few examples follow: number sequence 0 ab 1 aab 2 aabb 3 aaab 4 aabbb 5 aabab 6 aaabb (this is a duplicate of 4, a rotated inverse) 7 aaaab 8 aabbbb etc.

-- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/>

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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. -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/> Legalize Adulthood! <http://legalizeadulthood.wordpress.com> #!/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());

On Mon, 2011-01-03 at 14:17 -0700, Richard wrote:

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

The two images are different. I followed the directions in the Fractint docs and dropped the first and last characters before converting to binary. I don't know the technical basis for doing this, so I can't say whether one way is more correct. Jonathan

On Tue, 2011-01-04 at 19:55 -0700, Richard wrote:

Did your value give the image in wikipedia?

Reasonably well. There are some spots where the foreground seems to disappear. Jonathan