From kragen@dnaco.net Sat Jul  4 23:56:28 1998
Date: Sat, 4 Jul 1998 23:56:27 -0400 (EDT)
From: Kragen <kragen@dnaco.net>
To: fractint@xmission.com
Subject: new snowflake?
Message-ID: <Pine.SUN.3.96.980704234907.13172k-100000@picard.dnaco.net>
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I found a mildly interesting new way of drawing the Koch snowflake.
The normal way is to start from the inside and build out, approaching
the fractal curve itself in the limit.  Well, we can also start from
the outside and approximate inwards; maybe this is well-known, but it
surprised me.

Here are L-systems for doing it.  I think you might have to put them in
fractint.l to use them, but maybe the lsystem fractal type lets you
pick different L-system files.  I haven't tested them with Fractint,
but only with my own lsys code, which is implemented from specs in
fractint.doc.  (I still haven't converted this to C or added WMF
output, folks.  Sorry.)

inside_out_snowflake {
        angle 6
        axiom f+f+f+f+f+f+
        f=f+f--f+f
}

# Standard way has points at top and bottom;
# inside-out way has them at left and right.
# Here I try to overlap them.
# xf is a segment of the inside-out way;
# yf is a segment of the normal way.

double_snowflake {
        angle 12
        axiom +xf++xf++xf++xf++xf++xf++@q3+yf++++yf++++yf++++
        f=
        x=xf++xf----xf++xf
        y=yf--yf++++yf--yf
}

Have fun, folks.

Kragen