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*bY(-@@@@@@   @@@@   @@@@@   @    @  @@@@@@  @@@@@    @@@@ Y)-@@@@@@  @@@@@@  @@@@@@  @@  @@  @@      @@@@@@  @@  @@Y*-@@      @@  @@  @@  @@  @@@@@@  @@      @@  @@  @@    Y+-@@@@@@  @@  @@  @@@@@   @@@@@@  @@@@    @@@@@   @@@@  Y,-@@@@@@  @@  @@  @@@@@   @@  @@  @@@@    @@@@@     @@@@Y--@@      @@  @@  @@  @@  @@  @@  @@      @@  @@      @@Y.-@@      @@@@@@  @@  @@  @@  @@  @@      @@  @@  @@  @@Y/-@@       @@@@   @@  @@  @@  @@  @@@@@@  @@  @@   @@@@ Y17 by Jason J Railton in STOS Basic beY7 
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EFormers
*******

by Jason J Railton in STOS Basic



A demo of different fractals, drawn using the random technique normally
used on the Sierpinski Triangle.  With the Siepinski Triangle you move 
half-way to one of three corner points.  With others (the square Carpet,
or the Koch Snowflake), you move 1/3 of the way to the points.  With the
Koch curve, you move 1/sqr(2) and rotate by 45 degrees about the point.
My Koch Curve Plus uses 1/sqr(4) and a 22.5 degrees rotation to give a
smoother curve.

In freeform mode, use the mouse to plot points.  Plot three or less points
and you get the 1/2 scaled step.  Plot four or more, and the step is 1/3.

Try plotting six points for a snowflake, or eight points in a square (the
four corners and a point half-way along each side) for the square Carpet.

The triangle has three points at its corners, which attract with a scaling
Efactor of 1/2.

The square carpet has eight points (a square, plus mid-points along the
sides) which attract with a scaling factor of 1/3.

The Snowflake has six points (at the centre of each mini-snowflake), which
also attract with a scale of 1/3.

The Koch curve has two points (at the tips of the spiral arms), which
attract with a scaling factor of 1/sqr(2) and a rotation of +45 degrees
(left point) and -45 degrees (right point).

The Curve+ uses 1/sqr(4) and 22.5 degrees. 

The S-Curve is the Koch curve but with both attractors using the +45
degrees rotation.

The Cross (my invention) uses four points, each with a scaling factor of
1/sqr(2) and a rotation of 45 degrees.  I developed this one to put at
the top of my fractal Christmas tree when I sent it around the PCs at
work.

EThe fern is more complicated - it has one point at its tip with a slight
scale and a small angle.  This copies the base leaves of the fern up
along its length, getting smaller and curving over each time.  There are
also two points near the root that have a much smaller scaling factor
and rotations of +-90 degrees.  These turn the fern from the main form
into one of the two branches at the root.  My Christmas tree was based on
a similar form, but with a straight trunk, a horizontal compression to
squash the whole form to make the trunk, and some curvature added to the
lower branches.



Jason J Railton
April '97