Rock Valley College

Fractal Trees

Perhaps you have walked by these murals in the JCSM lower level and wondered "what in the world are these trees all about?" 

Each fractal tree mural is based on a different tree, and multiple copies of the trees were arranged to form the murals, which were designed by Demonica Kemper Architects. 

A fractal is an object exhibiting self similarity on different scales that can be related mathematically. Iteration, the process at the heart of fractals, is the repetition of a series of steps over and over to achieve an ever more detailed or more accurate result. The fractal trees depicted in the JCSM murals were constructed by iteratively arranging copies of a building block created from photographs of natural trees. The building block is designed so that smaller copies can be joined to a larger copy in seamless fashion. 

A set of rules specifying the scaling factor, rotation angle, and whether or not the smaller copy is mirrored (M), governs the arrangement of the smaller copies. After a large number of iterations, a fractal tree is obtained in which each branch, large or small, is an exact copy of the entire tree. An example illustrating the creation of one of the trees is shown below.

Step 1: The design  of the tree is planned out in a drawing program.

Fractal Trees Step 1.

Step 2: Photographs are taken of a tree (in Aspen in this case) that will approximately match the designed tree. The raw photographs are distorted, cropped, and assembled to form a rough building block.

Fractal Trees Step 2.

Step 3: The shading of the different parts of the tree is adjusted to allow seamless joining of smaller to larger copies. The image is trimmed around the outline of the tree to form the final building block. In this example, six smaller copies are added with each iteration.

Fractal Trees Step 3.

Step 4: Smaller copies are joined to the starting building block, where each copy is scaled, rotated, and possibly mirrored. Next, smaller copies of this composite structure are arranged around the building block in the same manner. This process is repeated 10-20 times to form the final tree.

Fractal Trees Step 4.

 

Students study in the lower level of the JCSM in front of the fractal tree murals.