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Model a Sunflower with the Golden Ratio

version (99.7 KB) by Joseph Kirk
Uses the Golden Ratio to predict the location of each seed on a sunflower


Updated 04 Mar 2016

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The Golden Ratio is sometimes called the Divine Proportion because it is often observed in nature, and some believe that it is God's signature.
The sunflower is one of those naturally occurring phenomena. This script demonstrates the connection between the Golden Ratio and the location of seeds on a sunflower.
The Golden Ratio is used in the calculation of the seed distance from the center as well as the seed angle. Compare this model with a true sunflower!
Note: It is well-documented that the Golden Ratio is observed in the angular
geometry of seeds in sunflowers, coneflowers and pinecones, as well as
other plants and natural phenomena. However, little regard has been paid, it seems, to the distance of each seed from the center. When I looked at sunflowers and coneflowers, I noticed that the density of seeds is not uniform throughout. Seeds toward the center are smaller than the seeds near the edges, and thus, their density is greater. This file makes a connection between the Golden Ratio and the seed distance from the center of the sunflower. This accounts for the growth of each seed over time, and provides a better model for seed location than linear distance from center.

Cite As

Joseph Kirk (2020). Model a Sunflower with the Golden Ratio (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (5)

ed churchill

In case you haven't seen them already, you might find these links helpful and interesting as well:

Felix TTTT

I like it for the purpose it has.

Joseph Kirk

There is an m-file (sunflower.m) ... I couldn't find a better category ... it was not a homework assignment but a personal interest that I wanted to share

Debbie M

I thought this was really neat! The graph looks like a pretty good approximation of the real picture. :)

John D'Errico

Sorry, but this one is not even an m-file, nor does it belong in this category even if it were. Its just a homework assignment on the golden ratio and sunflower seeds.


Updated Live Script

Updated Live Script

Added new live script

Updated description, information

Code vectorization

MATLAB Release Compatibility
Created with R2016a
Compatible with any release
Platform Compatibility
Windows macOS Linux