Vi Hart made an excellent series of videos related to plants and Fibonacci numbers. Here is the first one: https://www.youtube.com/watch?v=ahXIMUkSXX0. Links to the other ones can be found in the description.
I absolutely love Hart's presentation style in that video. It's so refreshing to see maths presented at a decent pace but still be easy to follow. And the quirkiness of the delivery only serves to make those videos more watchable.
Thank you for the recommendation. I'll definitely be subscribing to her channel :)
Another excellent source on this topic is a book I cited in the code comments called "The Algorithmic Beauty of Plants" by Prusinkiewicz and Lindenmayer, available online here: http://algorithmicbotany.org/papers/#abop