“theoretical fractals are infinitely (1) self-similar, (2) iterated, and (3) detailed mathematical constructs having fractal dimensions.” That’s fractals.”Īccording to Wikipedia the following definition is commonly adopted: Mandelbrot defined a fractal as “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.” His informal description may have been more accurate though: “ beautiful, damn hard, increasingly useful. Fractals come from the Latin fractus meaning ‘broken’. The term fractal was first used by mathematician Benoit Mandelbrot in 1975 in his book “ The Fractal Geometry of Nature“. Technically each branch junction (where one stem splits into more or ‘bifurcates’) is known as a ‘node’, and each branch is an ‘internode’. On a big tree you may be able to count as many as 11 Orders. For example, the main stem (or trunk) you would count as ‘1’, and when this has a branch count that as ‘2’, and when this branch produces a twig you would count this as ‘3’. On a young tree, say one about the height of you, it may have an Order of four or five.
Try and count how many times each stem splits into a smaller one – each one known as an ‘Order’.
Unless it is very young, your tree subject will repeatedly branch into smaller and smaller branches from the ground upwards. Go for a walk outside, if you can, and find a deciduous tree (a tree which looses its leaves in winter), or alternatively find a picture in a book or online. Did you know that most trees have no more than 11 orders of branches? To put it another way, trees grow in patterns known in math as ‘ branching fractals‘ and are usually limited to 11 internodes.
#Long play video fractal full
This time of year the bare branches of deciduous trees display their full beauty and fascinating growth patterns. My writing about art and math in nature are always among my most popular posts, and I’ve meant to write about fractals for a while because they fascinate me.