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Koch-like fractals

The images at the bottom of this page were created with <lxkoch<>.

The way <lxkoch<> works is very much like this way of describing how to create the Koch
Curve:

Start with this shape:

Then replace each of the 4 line segments in the shape, with a smaller version
of the shape:

<p
1)
      /\
     /  \
_/\_/    \____

2)
     _/\
    \   \
_/\_/    \____

3)
     _/\_
    \    /
_/\_/    \____

4)
     _/\_
    \    /
_/\_/    \_/\_
<>

Now we have 16 line segments, and we replace them all with even smaller
versions of the original shape. And again, and again. And again, and again.

<lxkoch<> works like this, except it allows you to create your own
shape. You can specify a shape made from 2 to 9 line segments (connected end to
end) and it will do as many iterations of this replacement process (described
above) as are necessary to get all the line segments down to less than a pixel
in length.  There are other programs that do this. I've seen one that works
with java right in a web browser. (links please?)

<lxkoch<> uses a unique (as far as I know -- <lJason Woofenden<>) rendering
method, which can create some astonishing images. Instead of just filling in
each pixel the line passes through solid white, this algorithm iterates until
the longest line segments are under .4 pixels long. Instead of filling in the
whole pixel, this algorithm just lightens the pixel according to how long the
line segment is. This makes it so that the more times the line crosses over
itself, the brighter it gets at that point.

<tkoch01.jpg<>

<tkoch02.png<>

<tkoch03.jpg<>

<tkoch04.jpg<>

<tkoch05.jpg<>

<tkoch06.jpg<>

<lxkoch<>

<lJason's Fractals<>

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