Nature is full of fractals. From sea shells and spiral galaxies to the structure of human lungs, the patterns of chaos are all around us. These fractals come in the form of branching and spiral patterns. Trees, ferns, the neurons in the brain, the blood vessels in our lungs, lightning bolts, rivers branching, as well as the coastline and rock formations are examples of branching types of fractals. Spiral fractals can be seen in the nautilus shell, weather patterns such as a hurricane, spiral galaxies, the spiral of pine cones and sunflowers.
Examples of fractals in nature:
Flowers, Ferns, Leaves, River channels, Lightning, Snowflakes are some of the examples of fractals in nature. Romanesco Broccoli a variant of cauliflower is the ultimate fractal vegetable. Its pattern is a natural representation of the Fibonacci or golden spiral, a logarithmic spiral where every quarter turn is farther from the origin by a factor of phi, the golden ratio. The Fibonacci sequence, a common and beautiful numeric pattern in nature creates the Golden Ratio.
Ferns are a common example of a self-similar set, meaning that their pattern can be mathematically generated and reproduced at any magnification or reduction. The mathematical formula that describes ferns, named after Michael Barnsley, was one of the first to show that chaos is inherently unpredictable yet generally follows deterministic rules based on nonlinear iterative equations. In other words, random numbers generated over and over using Barnsley's Fern formula ultimately produce a unique fern–shaped object. Many plants follow simple recursive formulas in generating their branching shapes and leaf patterns.