While Geometry often describes and measures shapes like a cone, sphere or triangle, does it define the shape of a cloud, a mountain, a coastline, or a tree?
|Starfish and Broccoli
are a few examples of fractal patterns in nature!
It does! Most patterns in nature, called “fractals” describe curves, surfaces and objects that have some very peculiar properties so irregular and fragmented, that it takes more than spheres, cones, circles, triangles, smooth or straight lines to describe them!
These fractals might resemble arteries, coral, a heart, a brain, tree branches and other such ‘designs’ that have symmetry, ‘self-similarity’ and are scale-free!
|Fern fractals – with symmetry
and self -similarity!
Look around you – Fractals are everywhere! Have fun with us and discover everyday Fractals at the upcoming RAFT workshop ‘Fractals and Beyond’ on Feb 9th, at RAFT San Jose. This workshop will demonstrate how fractals can be related to Sierpinski’s gasket, to patterns, to equations, to graphing, and to even a broccoli!
Break off a branch of the whole broccoli and what do you see? The smaller branch looks just like a miniature copy of the whole broccoli! Now think of self-similarity in ferns, the formation of shells, mountains, lightening, river estuaries, fault patterns, galaxies, musical compositions, and other nature’s designs.
A fractal’s dimension indicates its degree of detail, or crinkliness. Simple curves, such as lines, have one dimension. Squares, rectangles, circles, polygons and others have two dimensions, while solid objects such as cubes, spheres, and other polyhedra have three dimensions.
All those dimensions are integers: 1, 2, 3… But a fractal could have a non-integer dimension of 1.4332. By understanding fractal dimension, mathematicians can now measure shapes such as coastlines that once were thought to be immeasurable.
If you want to explore the world of Fractals, a science that marries Art with Math, join us for the upcoming workshop this week.
Discover your own fractal designs with RAFT’s Hands on Activity Kit ‘Freaky Fractals’!
Share your experiences with everyday Fractal patterns in nature here! Add your comments below.
Jeanne Lazzarini, RAFT Math Education Activity Developer