.:Nature's Hidden Art -
Images found in the mathematics of natural systems...
Photo "Oak Tree in Winter" by Snemann
Nature provides some striking images, visible records of
movement, like the fractal branching evident in the growth of an
oak tree as it fills the space allotted to it.
The visible Art of nature though is not the
whole story. The fluttering of an oak tree's leaf in the breeze
does not leave a permanent record of that motion but just out of
sight, one or two levels of abstraction below the visible, that
motion creates its own Art. It turns out that the complicated
motion of a fluttering leaf may be approximated by mathematical
expressions. Applying appropriate imaging algorithms to these
mathematical expressions we can create a portrait of the leaf's
behavior. This same technique applies to all physical objects in
motion, a bouncing ball, a satellite in orbit, ocean waves or
whatever.
Mathematical models of more abstract systems
are possible, population growth, the spread of disease, the life
cycle of a rumor and so forth. The behavior of these systems also
leads to striking images when properly displayed. In fact since
the images arise from the mathematics describing the systems, we
can generate images for systems that do not, as far as we know,
exist in nature.
The images displayed in the galleries linked
on this page are captured from actual moving objects like the
fluttering oak leaf or from made-up systems that so far as we
know exist only as mathematical expressions. The galleries are
organized according to the particular algorithm used to extract
the image from the mathematics of the systems. If you click on
one of the small images, shown below, you will be transported to
a small collection of images produced by the indicated algorithm.
Clicking on the small images in each gallery will present a
larger image and information on the mathematical system from
which the image came. If you have the time and are so inclined,
by following all the links in these pages you can get a pretty
good understanding of the system dynamics. Otherwise just enjoy
these crude sketches from natures portfolio. They are indeed
crude. The computer cannot begin to capture the fine detail of
the real image. The images below the navigation buttons are more
examples of nature's hidden Art.
The "Complex
Sets" and "Attractor
Mists" collections of images were produced by Ross Hilbert's
Fractal Science Kit. Click on the Fractal Science link for
details on how to get that program. The "3D Attractor" images were produced by
the Chaoscope program. Click on the Chaoscope link for details on how
to get that program, which is an ongoing project created and
maintained by Nicolas Desprez. The images in the remaining
galleries were created with a program called "Order" that we
wrote to help teach the mathematics of chaos. A limited version
of Order is available on this
site. Click on the link Order for a free copy
of the industrial strength version. Just run the OSetup.exe program to
install Order on your computer. You may need to agree to download and run
the program, depending on your security settings.
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