Description of Fractal Trees

This webpage explores angles through drawing trees.

When learning about angles, it helps to encourage students to look out for angles in normal life. Unfortunately, the right angle tends to dominate (corners of rooms, shape of computer screens, etc.) However, if you look at the branches of trees, you can find plenty of angles.

Imagine a tree without leaves, say, a deciduous tree in winter. One particular species of tree will have a particular shape, made from its branches. There will be the trunk, which will split into a number of branches, often a low number such as two. Then each branch sub-divides, and so on. When two branches grow out of a bigger branch, they will tend to be at a particular angle to it, and this will continue throughout the tree. This means that if you take a branch of the tree, together with all the smaller branches coming off it, and hold it upright, it looks rather like the tree itself. The tree is a fractal.

This webpage will draw a tree for you. You choose the angles between the branches, and watch as the tree grows. Then choose a different angle, and a different shaped tree will grow.

You can also choose the number of smaller branches growing from the bigger branch, and how big the smaller branches are:

2 branches Both branches are half the length of the branch they grow from. The angle chosen is the angle between them.

3 branches All three branches are half the length of the branch they grow from. The angle chosen is the angle between a side branch and the central branch.

2 branches The central branch is the same length as the branch it grows from. The side branches are half this length. The angle chosen is the angle between a side branch and the central branch.

After playing with the webpage for a little while, you might like to extend the idea. Try drawing your own tree. Youwill need a protractor, and you will get a lot of practice in using it! You might like to start by copying a tree from the screen, to get the hang of the idea. Then you can go onto to design their own trees. How many branches from each larger branch? What happens if the smaller branches are a different fraction of length to the larger branch, say two thirds rather than a half? If you have three branches, what happens if the central smaller branch is a different length from the side branches? And what does the tree look like if you add some leaves? If you look at an accurate book of trees, or even at a real tree, can you reproduce it using this technique? It won't be quite right, as trees live in three dimensions, not two, but it's fun to see how close you can get!

If it's too hard to draw trees yourself, try looking at real trees, and seeing the angles that their branches make with the tree trunk.

Click here for the Fractal Trees webpage.