Systems and objects in nature
that are radically changed by chaos
are called nonlinear. Artists have
recognized and interpreted nonlinear patterns for centuries. The
work of artist Nachume Miller
(1949–1998) is often interpreted as
fractals. He said that “Looking at
my work, you could see a seascape,
a microscopic cosmos . . . it could
be the Milky Way.” Fractal patterns
have also been discovered in sounds
of nature and music.
laws within dynamic systems such
as meteorology. However, they cannot always predict or exert control
over chaos. A unique set of geometric equations, the Mandelbrot Set,
express fractal patterns found in a
variety of natural and humanmade
objects. The repeated designs are
easily recognized
within geologic
features, plants,
and animals.
Fractals can be created
using mathematical
equations and computers.
Computers and Fractals
Fractals can be created using mathematical equations and computers.
Today, scientists use computers
to better understand chaos and its
Teacher Activity
In your classroom, using a PC, a digital projector, and a freeware fractal
generation program, select a fractal
pattern and experiment by zooming
in on chosen sections. Discuss how
fractals repeat themselves as you
continue to magnify the image. Use
the drop fractal generation program
to change the color schemes and
fractal equation parameters to create
additional patterns.
Remember to ask students to
make connections and identify
repeating shapes
found in nature.
Select student
volunteers to
make changes and
create their own fractal designs for
the class to enjoy. Copy the freeware
onto CDs, and use them in your
school’s computer lab. Independent
study will be a welcome event. Fractal print imagery could serve as a
substitute for interactive software.
