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The Lunar New Year is approaching and 2024 is the Year of the Dragon! This inspired me to create a visualization approximating the dragon curve in Maple Learn, using Maple. 

The dragon curve, first described by physicist John Heighway, is a fractal that can be constructed by starting with a single edge and then continually performing the following iteration process:  

Starting at one endpoint of the curve, traverse the curve and build right triangles on alternating sides of each edge on the curve. Then, remove all the original edges to obtain the next iteration. 

visual of dragon curve iteration procedure 

This process continues indefinitely, so while we can’t draw the fractal perfectly, we can approximate it using a Lindenmayer system. In fact, Maple can do all the heavy lifting with the tools found in the Fractals package, which includes the LSystem subpackage to build your own Lindenmayer systems. The subpackage also contains different examples of fractals, including the dragon curve. Check out the Maple help pages here: 

Overview of the Fractals Package  

Overview of the Fractals:-LSystem Subpackage 

Using this subpackage, I created a Maple script (link) to generate a Maple Learn document (link) to visualize the earlier iterations of the approximated dragon curve. Here’s what iteration 11 looks like: 

eleventh iteration of dragon curve approximation  

You can also add copies of the dragon curve, displayed at different initial angles, to visualize how they can fit together. Here are four copies of the 13th iteration: 

four copies of the thirteenth iteration of the dragon curve approximation 

 

Mathematics is full of beauty and fractals are no exception. Check out the LSystemExamples subpackage to see many more examples. 

 

Happy Lunar New Year! 

 

Featured Post

Maple Transactions frequently gets submissions that contain Maple code.  The papers (or videos, or Maple documents, or Jupyter notebooks) that we get are, if the author wants a refereed submission, sent to referees by a fairly usual academic process.  We look for well-written papers on topics of interest to the Maple community.

But we could use some help in reviewing code, for some of the submissions.  Usually the snippets are short, but sometimes the packages involved are more substantial.

If you would be interested in having your name on the list of potential code reviewers, please email me (or Paulina Chin, or Jürgen Gerhard) and we will gratefully add you.  You might not get called on immediately---it depends on what we have in the queue.

Thank you very much, in advance, for sharing your expertise.

Rob



order of elements in lists

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