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Fibonacci Art

Fibonacci Grid Activity on the Art Canvas Plus Playground with the VR Robot at the outer portion having filled in sections of the spiral.
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Challenge: The Fibonacci sequence is a pattern found all over nature. The way to calculate a number in the Fibonacci sequence is to add the previous two numbers together. A Fibonacci grid is a grid of squares where the side lengths of each square follow the Fibonacci sequence (for example, 1, 1, 2, 3, 5, 8, etc.). The object of this activity is to code the VR Robot to create a Fibonacci spiral on a Fibonacci grid by drawing quarter-circles in the corner of each square (The radius of each quarter-circle should be equal to the square side length.), then fill each quarter-circle with a specific color to create a unique piece of Fibonacci art!

  • Choose and download the Fibonacci Grid as a PNG file from this Google slideshow.
  • Select the Art Canvas+ Playground and upload the Fibonacci grid.
  • Declare three variables, n, b, and a, to represent the current number, the first preceding number, and the second preceding number respectively in the Fibonacci sequence. 
  • Code the VR Robot to create a Fibonacci spiral on the Fibonacci grid.
    • Initialize the values of variables n, b, and a. Use the variable n to determine the size of the quarter-circle.
    • Code the VR Robot to drive to the green Start Position at the Fibonacci grid.
    • Using the value of variable n, code the VR Robot to draw a quarter-circle in the corner of the Number 1 square with a radius equal to the square side length. 
    • Update the value of variable n to the next number in the Fibonacci sequence, and use it to code the VR Robot to draw a quarter-circle in the corner of the next square. Repeat this process to create a Fibonacci spiral on the Fibonacci grid.
  • Code the VR Robot to create Fibonacci Art.
    • Code the VR Robot to drive into each quarter-circle, and use the [Fill area with color] block to fill the quarter-circle with a specific color.

Helpful Hints

  • Use the variable n to determine the size of a quarter-circle. For example, you can code the robot to drive forward for n mm, turn 9°, and repeat these actions 10 times to draw the quarter-circle,
  • Adjust the initial values of the variable n to draw a quarter-circle with a radius equal to the side length of the Number 1 square. For example, set the initial values of variables n, b, and a to 22.5, 22.5, and 0, respectively. 
  • Update the value of variable n to the next number in the Fibonacci sequence according to the Fibonacci sequence rule: n = a + b, where n represents the current number, b represents the first preceding number, and a represents the second preceding number in the Fibonacci sequence.
  • Use the set block from the Variables category to update the values of the variables.Three VEXcode Set variable blocks in a stack. The first reads 'set a to b', the second reads 'set b to n', and the final one reads 'set n to a + b'.

    • Matching Python command:

      a = b
b = n
n = a + b
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