Part of what makes plants look so interesting is that their leaves are all the same shape.  Repeating similar (geometrically congruent) shapes are called "fractals" in mathematics.  Even though we use virtually no mathematics in making our Origami Bonsai sculptures, they have mathematical properties that make them look more interesting, and these properties are largely a result of fractals.

Another technique we employ in Origami Bonsai increases the perceived depth of our sculptures. The sculpture above seems to be deeper than it actually is.  Inceimentally sized leaves simulate a depth of approximately 10 inches when in fact the sculpture is only about four inches deep (it has five leaf sizes and three flower sizes).  This artificial increase in depth is another application of fractals.  Basically, the leaves closest to the viewer are the largest, and furthest away are the smallest.  The book "Advanced Origami Bonsai" has a clearer explanation, and detailed instructions for creation and assembly of depth enhanced origami bonsai.

Try thinking of it this way, when a painter paints a painting, objects that are closer to the viewer are painted larger, and objects further away are painted smaller.  We're basically doing the same thing in a depth enhanced origami bonsai sculpture, but more discretely.

Please click here for a clearer explanation of fractals.

Note to Educators and Parents:
Young children in Japan are exposed to Origami at a very early age because it teaches geometry in a subtle and fun way.  Consider exposing your child(ren) to origami bonsai (and fractals) when they are between nine and 13 years old.  This will allow them to explore  fractal mathematics in a discreet way and may stimulate future ideas for applications of fractals.

In general, origami bonsai stimulates high-order thinking and should result in better understanding of both mathematics and the world around us.