TimeTablesAdapted

1 collaborator

Kashif Zia (Author)

WHAT IS IT?

ADAPTED FROM http://modelingcommons.org/browse/onemodel/6859#modeltabsbrowsenlw 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 "go" 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

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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
end 

to go

  work-on mult
  ;let i 2
  ;while [i <= modulo][
  ;  work-on i
  ;  set i i + 1
  ;]
end 

to work-on [m]
  setup
  ask turtles [
    let parner (who * m mod modulo)
    if who != parner
    [create-link-with turtle parner]
    ask links [ set color cyan ]
  ]
  ;let name word m ".png"
  ;export-view name
end

There is only one version of this model, created over 2 years ago by Kashif Zia.

Attached files

File	Type	Description	Last updated
TimeTablesAdapted.png	preview	Preview for 'TimeTablesAdapted'	over 2 years ago, by Kashif Zia	Download

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