In my research, I have found that the fractals used most for plant growth are L systems. L systems use an alphabet and a set of rules to determine how the tree should grow. For example, a simple L system could be constructed by using an alphabet of A and B. The algorithm runs through the desired amount of generations and replaces the As with AB and the Bs with As. Then once the function is finished, the string of letters can be used as a set of instructions for drawing a tree. For example, A might mean to draw a line and B might mean to turn in a certain direction. With Houdini, you can specify differences of the instructions throughout the different generations, allowing you to create a very specific output. Another famous fractal I have come upon is the Mandelbrot set. This fractal is created by using a specific function with the output being a composition of the same function. The result is a mesmerizingly intricate design.
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