Reading about golden number and the singularity of certain shapes in nature, I found a lot of articles about a Maths´concept: the fractals. I´m sure that your teacher would explain you better than me what´s about these beautiful structures. But I´ll try to define it: a fractal is a pattern inside the structure of some objects and shapes so, it displays a self-similarity on all scales.
That term that represents a graphic and mathematical model was suggested by Benoit Maldelbrot in 1973, (for learn more http://en.wikipedia.org/wiki/Benoit_Mandelbrot) who used computers to create geometric shapes from chaos to order.
The concept are close up related to Golden ratio. For instance,the proportions of different plant components (numbers of leaves to branches, diameters of geometrical figures inside flowers) are often claimed to show the golden ratio proportion in several species but in some of these "magic" repetitions it´s possible to find fractal models.
"Romanesco broccoli, or Roman cauliflower, is an edible flower of the species Brassica oleracea, and a variant form of cauliflower. First documented in Italy, it is light green in color and is a natural approximation of a fractal." (from WIKIPEDIA)
A pasionate article about the topic:http://www.tyrantfarms.com/garden-golden-ratio-fibonacci-sequence/#.Ukc2YtLwmSo
My students, you are going to learn a lot about Gestalt Laws along next weeks. What is Gestalt Psychology? Click here-
Well, in fact, in the case of fractals you can see that the formation of a continous pattern is based on the law of SIMILARITY.
" law of similarity - a Gestalt principle of organization holding that (other things being equal) parts of a stimulus field that are similar to each other tend to be perceived as belonging together as a unit" (from http://www.thefreedictionary.com/law+of+similarity)
Searching in the Net, it is easy to find " fractal Generators", computer application by means of it, you will create a huge amount of marvellous fractals, e.g. http://www.easyfractalgenerator.com/