Fractals and nature

Math is the greatest thing ever invented.

Numbers give me comfort, they are always there, they never betray you. They have a reason to exist and answers to most questions.







Shown here, the stage-4 Sierpinski tetrahedron provides a powerful visual introduction to fractal geometry and the concept of "self-similarity", in which a shape can be broken into smaller copies of the whole. Each new stage is composed of 4 smaller copies of the previous stage. As the number of stages increases, the Sierpinski tetrahedron approaches "exact self-similarity".
Such geometric fractals provide an important scientific model for characterizing many of the complex processes and shapes found in the natural world, that are echoed in the settings of the tetrahedra. Trees, land formations, clouds, and their images exhibit "statistical self-similarity" in which a small part "looks like", but not "exactly like" the whole. Just as a part of the Sierpinski tetrahedron reminds one of the whole, a small branch of a tree reminds one of the entire tree.
The mathematics of fractal geometry and the science of chaos are now bridging the gaps between math, science, art, and culture. They treat the messiness of the everyday world. They are based on natural self-similarity and observations of complicated behavior from simple equations. They provide a new mathematical language for capturing, manipulating, and simulating nature.