Wildfire (with colors)

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Default-person Yunus Arabacigil (Author)
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Model was written in NetLogo 6.4.0 • Viewed 4 times • Downloaded 0 times • Run 0 times
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WHAT IS IT?

Color Fractions displays the decimal form of a fraction as a pattern of colors. This lets you investigate how the resulting patterns relate to the original fraction.

HOW IT WORKS

The program computes the digits of the decimal the same way you would do it using long division on paper.

It takes the numerator and divides it by the denominator; the result is a digit. The remainder of the division, we multiply by 10 and take as the new numerator, then repeat.

For example these would be the steps for computing 1/7:

  • 7 goes into 1 0 times; 10 times remainder is 10
  • 7 goes into 10 1 time ; 10 times remainder is 30
  • 7 goes into 30 4 times; 10 times remainder is 20
  • 7 goes into 20 2 times; 10 times remainder is 60
  • 7 goes into 60 8 times; 10 times remainder is 40

And so on forever. Thus the result is 0.1428...

To make the pattern of colors, each digit, 0 through 9, is shown in its own color. For example 0 is gray, 1 is light red, 2 is orange, etc.

HOW TO USE IT

Press the SETUP button, then press GO.

Now adjust the numerator and denominator sliders to make any fraction.

You can also use the WIDTH slider to change the total number of digits per row. Changing the width can make patterns easier or harder to see.

THINGS TO NOTICE

The same fraction always gives the same pattern.

Some patterns stop after a few digits, while others repeat forever. (Do all fractions repeat?)

Do two fractions ever give the same pattern?

THINGS TO TRY

What kinds of patterns can you generate with fractions? Can you create a checkerboard? Can you make vertical stripes?

What happens if you try different numerators with the same denominator? What do the patterns you get have in common? Try this experiment with several different denominators.

The "period" of a fraction is how many digits repeat to make the pattern. For example, 1/3 is 0.33333... which repeats the same single digit over and over again, so the period is 1. Look at the pattern for the fraction 1/7; the period is 6. And so on.

How is the period of a fraction 1/n related to n? How are the periods of the fractions family 1/7, 2/7, ... related?

How many fractions can you find that have the same number of repeating digits?

What fraction best approximates pi (3.141592...)?

EXTENDING THE MODEL

Change the colors so odd numbers are all one color and even numbers are another color.

Change the colors so you only use one color, but vary the lightness/darkness.

Modify the program so you can visualize square roots and pi.

NETLOGO FEATURES

Patch labels are used to show the digits.

You can use the sort primitive to created a list of patches sorted left-to-right, top-to-bottom. That is necessary in this model because we need the patches to execute in the same order at every tick, rather than a different random order every tick as would happen if we just said ask patches.

RELATED MODELS

Division

CREDITS AND REFERENCES

This model is adapted from a few resources that are no longer available: Color Calculator Information for teachers and Color Calculator.

This model implements activities originally published in: Nathalie Sinclair, Rina Zazkis and Peter Liljedahl. Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts. International Journal of Computers for Mathematical Learning, Volume 8, Number 3, pages 235 - 263, January 2003.

HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

Please cite the NetLogo software as:

COPYRIGHT AND LICENSE

Copyright 2005 Uri Wilensky.

CC BY-NC-SA 3.0

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

Comments and Questions

Please start the discussion about this model! (You'll first need to log in.)

Click to Run Model 

; Wildfire (Risk-Weighted) — fixed setup order

patches-own [
  burning?
  burnt?
  ignition-tick
  fuel
  risk
]

to setup
  clear-all
  setup-terrain
  compute-risk-all
  reset-ticks           ;; <-- moved here
  seed-initial-fires
end 

to setup-terrain
  ask patches [
    set burning? false
    set burnt?   false
    set ignition-tick -1
    set fuel (fuel-density * random-float 1)
    set pcolor green
  ]
end 

to go
  compute-risk-all
  step-spread
  step-burning-lifecycle
  step-spontaneous-ignitions
  tick
end 

to compute-risk-all
  let wf risk-fuel-weight
  let wd risk-dryness-weight
  let ww risk-wind-weight
  let wsum (wf + wd + ww)
  ask patches [
    let dryness (1 - humidity)
    let base (wf * fuel + wd * dryness + ww * wind-strength)
    ifelse wsum > 0
      [ set risk clip01 ( base / wsum ) ]
      [ set risk clip01 (fuel * (1 - humidity)) ]
  ]
end 

to seed-initial-fires
  let candidates patches with [ (not burnt?) and (not burning?) and (risk >= ignition-threshold) ]
  if any? candidates [
    ask n-of min (list initial-seeds count candidates) candidates [ ignite ]
  ]
end 

to step-spontaneous-ignitions
  ask patches with [ (not burnt?) and (not burning?) and (risk >= ignition-threshold) ] [
    let p (spark-rate * risk)
    if p > 1 [ set p 1 ]
    if (random-float 1) < p [ ignite ]
  ]
end 

to step-spread
  ask patches with [ burning? ] [
    ask neighbors with [ (not burnt?) and (not burning?) ] [
      let bearing ((towards myself + 180) mod 360)
      let diff subtract-headings wind-dir bearing
      let r diff * pi / 180
      let w (1 + wind-strength * cos r)
      if w < 0 [ set w 0 ]
      let p (spread-prob * risk * w)
      if p > 1 [ set p 1 ]
      if (risk >= ignition-threshold) and ((random-float 1) < p) [ ignite ]
    ]
  ]
end 

to step-burning-lifecycle
  ask patches with [ burning? ] [
    if (ticks - ignition-tick) >= burn-duration [
      set burning? false
      set burnt?   true
      set pcolor black
    ]
  ]
end 

to ignite
  if burnt? or burning? [ stop ]
  set burning? true
  set ignition-tick ticks
  set pcolor red
end 

to mouse-ignite
  if mouse-down? [
    let p patch mouse-xcor mouse-ycor
    ask p [
      if (not burnt?) and (not burning?) and (risk >= ignition-threshold) [ ignite ]
    ]
  ]
end 

to-report clip01 [x]
  if x < 0 [ report 0 ]
  if x > 1 [ report 1 ]
  report x
end

There is only one version of this model, created 2 days ago by Yunus Arabacigil.

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