 D. H. Hepting
 Projects
 Math Art
 Fractals  Nature's Numbers?
Fractals: Nature's Numbers?
by Daryl Hepting
Can numbers describe nature?
Finding numbers to describe nature can bring to it a sense of order.
Some examples from history include:

musical scales (doubling frequency increases octave,
also related to length of string)

development of sunflower heads
(Fibonacci numbers and Golden Angle describe placement of seeds)
Can numbers describe coastlines or clouds?
Fractal dimension
Look at this progression of shapes. Can you see a pattern?
Think of the original line in 3 segments. Replace those 3 segments with 4
segments, as shown in the second curve. Repeat.
The dimension of this curve: log4 / log 3.
Nature's dynamics
The natural world is filled with dynamic processes:
 Predator/Prey relationships in the wild (modelled by LotkaVolterra
equations)
 The
Butterfly Effect (describing the potential impact on global weather
of the flapping of a single butterfly's wings)
 Symmetry
in Chaos (the work of Golubitsky and Field: finding patterns in
the averaging of millions of iterations)
 The Mandelbrot Set: complexity from a simple equation
Forgeries or the real thing?
Mandelbrot, the father of fractal geometry once said:
clouds are not spheres,
mountains are not cones,
coastlines are not circles,
and bark is not smooth,
nor does lightning travel in a straight line ...
Can you see any similarities between these following two video clips?