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Fibonacci Spiral

Fibonancci Spiral

The Fibonacci Spiral Model draws a geometric spiral whose growth is regulated by the Fibonacci series. Its growth parallels the rapid growth of the series itself. The golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.  To produce a uniform distribution in the plane of the spiral, points are separated by the golden angle.

 

This model is designed to test OSP 3D drawing implementations in EJS.  The sprial can be drawn using the Simple 3D implementation that run using only standard Java.  The Java 3D implementation of the library provides superior hardware-acclerated drawing of geometric objects such as spheres, but requires that the Java 3D package.  This package can be downloaded from the Java community website.

Credits:

The Fibonacci Spiral Model was developed by Wolfgang Christian using the Easy Java Simulations (EJS) version 4.3.7 authoring and modeling tool. 

 

You can examine and modify a compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open Ejs Model" from the pop-up menu.  You must, of course, have EJS installed on your computer.  Information about Ejs is available at: <http://www.um.es/fem/Ejs/> and in the OSP comPADRE collection <http://www.compadre.org/OSP/>.

 

For Teachers

Translations

Software Requirements

SoftwareRequirements

Android iOS Windows MacOS
with best with Chrome Chrome Chrome Chrome
support fullscreen? Yes. Chrome/Opera No. Firefox/ Sumsung Internet Not yet Yes Yes
cannot work on some mobile browser that don't understand JavaScript such as..... cannot work on Internet Explorer 9 and below

 

Credits

Wolfgang Christian - Davidson College; Tan Wei Chiong; Loo Kang Wee

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Sample Learning Goals

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For Teachers

In this simulation, the number of points n can be adjusted with either the slider or the field provided. Similarly, the size of the points can be adjusted with another slider/field pair.

The numbers on the points corresponding to the sequence in which they are generated can be toggled on and off using the checkbox on the top left, and a table showing the coordinates of each point can also be toggled with the checkbox beside it.

Do play around with the simulation to try to find the Fibonacci numbers hiding within!

Research

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Video

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 Version:

  1. http://weelookang.blogspot.sg/2016/02/vector-addition-b-c-model-with.html improved version with joseph chua's inputs
  2. http://weelookang.blogspot.sg/2014/10/vector-addition-model.html original simulation by lookang

Other Resources

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