By Jeanne Lazzarini, Math Master Educator/R&D Specialist, RAFT
How does math relate to real life? One way is to take a look at the shape of a cloud, a mountain, a coastline, or a tree! You might be surprised to find that many patterns in nature, called fractals, including growth patterns, have very peculiar mathematical properties --- even though these natural shapes are not perfect spheres, circles, cones, triangles, or even straight lines!
|3D Fractals For Inspiration|
So, what is a fractal? Benoit Mandelbrot (November 20, 1924 – October 14, 2010) is commonly called the father of fractals. He created the term “fractal” to describe curves, surfaces and objects that have some very peculiar properties. A fractal is a geometric shape which is both self-similar and has fractional dimension.
Ok, so what does that mean? Well, “self-similar” means that when you magnify an object, each of its smaller parts still look much the same as the larger whole part. And, “fractal dimension” is different from what we use to describe shapes such as lines, flat objects, and geometric solids. Simple curves, such as lines, have one dimension. Squares, rectangles, circles, polygons, etc. have two dimensions, while solid objects such as cubes and polyhedra, have three dimensions. Some say time is the fourth dimension. In all these cases, dimension, based on Euclidean Geometry, is described as an integer: 1, 2, 3, 4, …
But a fractal curve could have a dimensionality of 1.4332, for example, rather than 1! A fractal’s dimension indicates its degree of detail, or crinkliness and how much space it occupies between the Euclidean Geometric dimensions. Most objects in nature aren’t formed of squares or triangles, but of more complex fractal shapes, such as ferns, flowers, coastlines, clouds, leaves, trees, mountains, blood vessels, broccoli, weather, lightening, fluid flow, river estuaries, circulatory systems, geologic activity, fault patterns, planetary orbits, animal group behavior, music, and so forth.
Whew! By understanding fractal dimension, mathematicians can now measure forms that once were thought to be immeasurable!
|Romanesco broccoli fractals|
Have fun discovering “fractals” with RAFT’s “Freaky Fractals” activity kit! Use the kit to create a fractal shape resembling “arteries”, “coral”, “a heart”, “a brain”, “tree branches”, etc. Then go to the store, buy some broccoli or cauliflower, then take a close look! Break off a branch and what do you see? The smaller branch looks just like a miniature copy of the whole vegetable! Now look around you and you’ll notice thousands of living examples of self-similarity in ferns, coastlines, clouds, leaf veins, trees, and the formation of shells, mountains, blood vessels, lightening, river estuaries, circulatory systems, fault patterns, galaxies, musical compositions, and so forth! By understanding fractal dimension, mathematicians can now measure shapes, such as coastlines and so forth that once were thought to be immeasurable! Fractals are AWESOME! Math really is all around you when you stop to look!