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February 2nd is Groundhog Day in North America. A day when we look to small marmots to prognosticate the weather. If the groundhog sees its shadow when it emerges from its burrow, then it predicts 6 more weeks of winter, and if not, then spring begins today! Unfortunately there are many official weather predicting groundhogs. Fortunately, the excellent website Groundhog-Day.com tracks each of their predictions. Unfortunately, it doesn't tell you which groundhog to trust. Fortunately, it has an API and we can take the data and map it in Maple:

This map assumes that each groundhog's prediction is valid at it's exact geographic coordinates, but that it's predictive powers fall off in inverse proportion to the distance away.  So, exactly halfway between a groundhog predicting early spring, and one predicting 6 more weeks of winter, we expect 3 more weeks of winter.  I handle that with Maple's Interpolation:-InverseDistanceWeightedInterpolation command with a radius of 1500 miles.  I plot a contourplot of that interpolating function, and then display it with the world map in DataSets:-Builtin:-WorldMap to generate the image above.

All the code to do that can be found in the following worksheet which also using the URL packaget to fetch the most recent groundhog data possible from the website.

Groundhog-Map.mw

I've commented out a few lines that you might use to explore other possible maps.  You can filter to file to just include real living groundhogs and not all the other precitions (some from puppets, some from other animals) if you find that more trust worthy. You might also prefer to change the interpolation command, one of my collegues suggests that Interpolation:-NaturalNeighborInterpolation might be a better choice.

Featured Post

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! 

 



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