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Polygonal Mandalas

Make colorful mandala-like designs.

Run the code to draw a line through the 5 points of a pentagon (5-sided polygon). Try a different number of points:

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CirclePoints gives points evenly spaced around a circle.

Draw the 5 corners of a pentagon (5-sided polygon):

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Connect the points with a line:

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The bottom of the pentagon is missing because the line is drawn from the first point to the last point, but not back to the first point again.

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Draw a line joining each pair of points. Try a different number of points:

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This gives a list of every pair of numbers (2-tuple) drawn from the list {1,2,3}:

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This gives a list of every pair of points drawn from the list of three points evenly spaced around a circle:

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Map (/@) applies a function, like Line, to every element of a list.

Draw a line connecting each pair of points:

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Show pictures for successively more points. Try starting and ending numbers other than 4 and 20:

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Table makes lists of things.

This makes a list of numbers from 4 to 20 in steps of 1:

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This makes a list of figures with 4 to 20 points:

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Make it interactive. Drag the slider to change the number of points:

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Replace Table with Manipulate to get a slider that you can control the number of points with:

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Make it colorful:

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Were going to need a few new concepts to make a colored line figure. Lets take it in small steps.

A pure function is a function that doesnt have a name.

This pure function (indicated by # and &) adds 1 to a number:

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Use the pure function with Map (/@) to add one to every number in a list:

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An equivalent way to write the same thing is to use the function Map instead of the /@ shorthand:

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MapIndexed is like Map. In fact, you get the same result if you use MapIndexed instead of Map:

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But MapIndexed makes the list position of each element the function is applied to available to the function. Use #2 to get the position:

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Use First to extract the position number from the list:

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Youll use the list position to specify the colors of lines in a line figure.

Hue gives different colors for different values between 0 and 1:

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You can use Hue to color objects in Graphics:

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Now you have all the concepts you need to color the lines in a figure.

This is the basic figure with black lines:

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Use MapIndexed to color the lines according to their positions in the list. Dividing the Hue value by 12 gives 12 different colors of lines.

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Add color to the interactive figure:

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Share ItMake a website with an interactive mandala:

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Deploy the Manipulate to the Wolfram Cloud where anyone with a browser can use it:

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Click the link in the output to visit the site.

Share the link by right-clicking it and choosing Copy Address. Paste the link into an email, tweet, or other message.

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