Just look at this awesome image, and then get a fresh cup of coffee and dig a little deeper.
You could begin by checking out fractals on Wikipedia. The boring and (at least to me) barely comprehensible maths about how fractals are formed might be interesting to you. But I would skip it for now
Or you could Google fractals in nature (plus images) and find an absolutely awesome introduction to the art and architecture in leaves and seeds and feathers and just about everything that grows! But I am not going to do that either.
I am going straight to one of my favourite sites, the website of Sven Geier and follow the links. His story fascinates me. The awesome computer generated images are breath takingly beautiful… visual inspiration to start a grey and rainy day with wonder and joy! And, even better, here is a link to animated fractals by Geier, each image morphing into a variation!
I hope it will amuse you as well!
And if (when?) you want to know more, go back and check the wiki link, and search Google images for the many, many other unbelievable images from the computer, and from the backyard!