Building a Koch Snowflake

• Our goal for the day
• Reference.
• This is a fractal example.
• To build this snowflake
  • Each line segment is replaced by:
    • A line segment from the start to 1/3 of the way in.
    • A line segment from 1/3 to the equivalent at a $60^\circ$
    • A line segment from the last to a point 2/3 of the way along the original line.
    • A line segment from 2/3 of the way to the final point.
• There are a few techniques and a little math involved in displaying this.
• Points or vectors?
  • I tend to go back and forth in my mind.
  • When I need linear items, they are vectors
  • Other times they are points.
  • I'm not sure this totally make sense but let's look at a few functions.
• In Distance this is the classic distance formula, and the input is definitely points.
• In OnLine I am thinking in a vector mode.
  • This generates a point a distance along the line.
  • IE 1/3 of the distance, 1/2 of the distance and 2/3 of the distance.
  • It just computes a vector the length of the line segment.
  • And then travels a distance along that vector.
• In FindPerp I think I am thinking more in a vector mode.
  • This finds the perpendicular line to a given line at a point.
  • Remember the slope of a perpendicular is $\frac{-1}{m}$
  • But I don't know how far along that line to go at first.
  • So I create a unit vector perpendicular to the given line, at the second end point.
  • To do this
    • Calculate one of the deltas as a negative.
    • Make the deltas a unit vector.
    • Add the deltas to the second end point.
  • Finally I move along the new line the required distance to a new point.
• The the starting points are based off of the canvas width and height.
• The computing of the curve is iterative, but it could be recursive.