Math behind the tiny planets from The little prince

I was browsing through a mathematical journal when I came across a title Mathematics in photography. That  immediately sparked an interest in me because I love playing with my camera. Have you ever seen a picture like the one below on the left? They always confused me because I didn’t have a clue how they were made. I thought that it couldn’t be easy. But I was wrong. 🙂 I will show you that mathematics is the key part in creating this kind of photos and in the end I will show you how you can do one yourself.

But let’s start at the beginning. Where does the title of this post come from? If you had read The little prince, then you probably agree that the above picture on the left resembles the tiny planets from The little prince. That’s where the title comes from! 🙂

Ok, let’s start. The key part in creating this kind of photos is a stereographic projection. What is this? It’s one of the ways of drawing the surface of the Earth on a piece of paper to create a map. Let’s see how that works.

Imagine an elf standing on the North Pole and holding a red flashlight. He is pointing the flashlight (through the Earth) towards South Africa. We project the point on the Earth, where the red light beam exits the Earth, to the point, where the same red light beam hits the piece of paper, which is placed under the Earth. One the right picture below you can see part of the map of the Earth made by the stereographic projection (Australia is the top continent, Africa is the continent on the right and South America is the continent on the left).

Now let’s go back to our planets. Imagine that the Earth is empty and that you are standing at it’s cor. All that you can see around yourself is the surface of the Earth. Now imagine that you are standing on a spot with a beautiful view. Close your eyes and pretend you are at the center of an empty ball, on the surface of which you see everything that is around you. Now open your eyes and take a panoramic picture because you love the view. Let’s say you took this picture.

If we pretend that this is actually everything that you can see around yourself, then the empty ball you had to imagine before looks like below.

This is now our “Earth” and we can draw the map of this “Earth” by using the stereographic projection. And this is how the tiny planets are created. 🙂

We crop the above picture to make it look more like the first picture in this post.

And this is it! 🙂 If you want to create your own tiny planets, you don’t need to know all this because mobile applications can do it for you. Here are a few suggestions for applications:

– Small planet (Android, free)

– Mini-Planet (Android, free)

– Tiny Planet (iOS, 0,89 eur)

– My photo planets (iOS, free)

Now you are ready to create your own tiny planets. If you like, you can share some of your masterpieces with me on my Facebook page. If you need some inspiration, I recommend this page. Enjoy! 🙂

P.S. There is another photo effect which is similar to the Tiny Planet Effect. It’s called the Rabbit Hole Effect. You can read about it here.