Fractals – Dragon Curve

Acrylic ornament - Dragon FractalNature creates perfect shapes.  These shapes, although appearing random, obey mathematical principles.  Many of the shapes in nature can be categorized as fractals.  Defined, a fractal is a geometric shape that is created by subdividing a shape according to some iterative process.  We see fractals in snowflakes, ferns, mountains, erosion patterns, and other places in nature.  There are many types of fractals, including legal circles, dragon curve, Sierpinski carpet, and Sierpinski triangle to name a few.  The one I will discuss here is a Dragon Curve.

A Dragon Curve fractal typically consists of a single line segment.  When starting, make a note of the beginning and end of the line.  That line segment is copied and rotated around the end point of the original line to generate a new image.  The new image is then copied and rotated around the end point of the previous image to create a new image.  The process is iterated until the fractal is as complex as you want.  New shapes can be created by varying the angle between the initial two lines.  Often, the Dragon Curve fractal is drawn with a starting point of two lines at right angles to each other (step two in the iteration).

See the images below for the steps in drawing a Dragon Curve fractal

If this looks confusing, it’s simpler that it first appears.  Just remember to keep track of the start and end of the segment, copy the original, and rotate the copy 90 degrees (or another angle) around the end point.  Your initial starting point never changes so your ending point is fairly easy to locate.  The more times you iterate, the more complex the design.

That is the basics of the Dragon Curve fractal.  There are many other fractal pattern and an internet search will lead you to more information than you could imagine on the subject.  I hope you learned something new here and go out and try to draw your own Dragon Curve fractal.  Good Luck!

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  1. [...] mountains, erosion patterns, and other places in nature.  There are many types of fractals.  In a previous post, I described the Dragon Fractal.  In this post, I will discuss here is a Legal Circle [...]