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:
CirclePoints gives points evenly spaced around a circle.
Draw the 5 corners of a pentagon (5-sided polygon):
Connect the points with a line:
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.
Draw a line joining each pair of points. Try a different number of points:
This gives a list of every pair of numbers (“2-tuple”) drawn from the list {1,2,3}:
This gives a list of every pair of points drawn from the list of three points evenly spaced around a circle:
Map (/@) applies a function, like Line, to every element of a list.
Draw a line connecting each pair of points:
Show pictures for successively more points. Try starting and ending numbers other than 4 and 20:
Table makes lists of things.
This makes a list of numbers from 4 to 20 in steps of 1:
This makes a list of figures with 4 to 20 points:
Make it interactive. Drag the slider to change the number of points:
Replace Table with Manipulate to get a slider that you can control the number of points with:
Make it colorful:
We’re going to need a few new concepts to make a colored line figure. Let’s take it in small steps.
A pure function is a function that doesn’t have a name.
This pure function (indicated by # and &) adds 1 to a number:
Use the pure function with Map (/@) to add 1 to every number in a list:
An equivalent way to write the same thing is to use the function Map instead of the /@ shorthand:
MapIndexed is like Map. In fact, you get the same result if you use MapIndexed instead of Map:
But MapIndexed makes the list position of each element the function is applied to available to the function. Use #2 to get the position:
Use First to extract the position number from the list:
You’ll 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:
You can use Hue to color objects in Graphics:
Now you have all the concepts you need to color the lines in a figure.
This is the basic figure with black lines:
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:
Add color to the interactive figure:
Share It—make a website with an interactive mandala:
Deploy the Manipulate to the Wolfram Cloud, where anyone with a browser can use it:
Click the link in the output to visit the site.
Tell the world about your creation by sharing the link via email, tweet or other message.