A simple way to show the Fibonacci numbers is to generate them in a loop and then show each number as the game score. The Fibonacci tiles are sprites that have square images. The square image sides are the length of the current Fibonacci number. As each square sprite is created, they are placed next to the previous square in a counter-clockwise pattern. To do this, we use a 4 step rotation sequence that places the new squares next to the previous square in the right location.
The current rotation step is kept in the rotation variable. A complete rotation happens in 4 steps so the rotation variable is reset to 0 after the square sprite is placed in rotation step 4. We have to remember the location of each previous sprite so that the next sprite is placed at the proper location.
The previous sprite is saved in the fibSprite0 variable. We can add a Fibonacci spiral to the squares in the program above using a function to draw arcs. The function can use the current value for the Fibonacci number as the arc radius. It follows the rotation sequence to know the direction to draw the arc. The arcs are drawn in the images for the squares using random dots that paint the arc line. Add the drawArc function to the previous program and call the the function just before updating the previous Fibonacci sprite:.
The squares and the spiral will eventually fill outside the view of the screen. To see all of the squares you can add code to scroll the screen view. The following code uses the arrow buttons to change the camera view center in order to scroll the screen view in 4 directions. The Fibonacci spiral equally has popularity outside India. Fibonacci spiral is based on the Fibonacci sequence and each quarter in the spiral is as big as the last two quarters.
The Fibonacci spiral equally crates the golden ratio, which is used for formatting purposes and applications by many smartphones and televisions. Research has shown that the faces of many of the celebrities out there today have a strong match to the ratio. The golden phi or number is 1. This simply means that each of the curves on the Fibonacci spiral will end up being 1.
The golden ratio represents the ratio of all the sides that make up a rectangle. If a square with sides represented by the smaller sides of the rectangle is removed from the rectangle, the rectangle remaining will still have sides having the same ratio. A golden ratio is never a transcendental number, unlike popular numbers like the e and pi. As a result, a finite number of exponentiations, divisions, multiplications, subtractions, additions or integers cannot be used in representing it.
Also, the Fibonacci spiral can serve as the base for representing positive integers expressed in a non-repeating form, which is usually referred to as metallic series. The golden ratio is also depicted by European paper sizes, making it easy to scale a paper size up or down.
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