TimesTables

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Jesus_marcano Jesus Marcano (Author)
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Model was written in NetLogo 6.2.1 • Viewed 251 times • Downloaded 5 times • Run 0 times
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WHAT IS IT?

This experiment reproduces the patterns explained in the YouTube video "Times Tables, Mandelbrot and the Heart of Mathematics" https://youtu.be/qhbuKbxJsk8 of the series Mathologer. It visualizes a multiplication table modulo the number of points distributed along the circuference of a circle. Many interesting patterns are formed, some of them are recognizable Mandelbrot patterns.

HOW IT WORKS

A number of points are distributed uniformly along the circumference of a circle, each labeled with an index arranged in ascending order from 0 to the number set by the slider labeled "modulo". A multiplication table is produced by multiplying the factor set by the slider labeled "mult" and the index of each point modulo the number of points. The result at each point is taken as the index of another point on the circumference and these two points are then joined with a straight line.

HOW TO USE IT

Set the slider "mult" to the fixed factor of the multiplication table. The other factors are the points (their indexes). Set the slider "modulo" to the number of points desired. The multiplication table is formed multiplying the factor set in "mult" by the index of each point modulo the value set in "modulo". Press "setup" to run the program.

THINGS TO NOTICE

Notice that the "mult" factor does not exceeds the "modulo" value. Allowing to do so would only repeat the same patterns.

THINGS TO TRY

Try to repoduce some of the patterns shown on the video of Mathologer cited above.

Comments and Questions

Excellent

Excellent visualization with just a few lines of code. I wonder can it be useful in applications or research.

Posted about 3 years ago
Click to Run Model 

to setup
  clear-all
  set-default-shape turtles "dot"
  create-turtles modulo
  ask turtles [ set size 0 ]
  layout-circle sort turtles max-pxcor

  ask turtles [
    let parner (who * mult mod modulo)
    if who != parner
    [create-link-with turtle parner]
    ask links [ set color cyan ]
  ]
end

There is only one version of this model, created about 3 years ago by Jesus Marcano.

Attached files

File Type Description Last updated
TimesTables.png preview Preview for 'TimesTables' about 3 years ago, by Jesus Marcano Download

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