Fibonacci Flower
The Fibonacci sequence is a pattern formed by the addition of the previous two numbers in the succession (beginning with 0 and 1). It is found throughout the natural world and the spiral pattern on sunflower seeds is no exception. If the spirals are counted in a consistent manner from the centre outwards a Fibonacci sequence will always emerge. 137.5° is approximately the golden angle of the spiral in which the Fibonacci flower is produced. Count the number of similar spirals spanning a circle, they add to values of the Fibonacci sequence!
For more information check out this Mathologer
video.
The buds within the flower are generated by the following equations, where n is an increasing natural
number and angle is the input angle:
a = n × angle ,
r = √n
x = r × cos(a) ,
y = r × sin(a)
The spiral line paths are determined by a simple shortest distance algorithm, and thus it fails to show all
possible spirals.
Toggle off Show spirals to find your own spirals by clicking on the buds.
"The path isn't a straight line; it’s a spiral. You continually come back to things you thought you understood and see deeper truths."
Create your own flower by varying the angle!
Must be greater than 0.
Visualisation by Harris Perdikoyiannis and William Zhang
Page authors: James Vereker, William Zhang and Harris Perdikoyiannis