| A forgery
of an object is a copy, meant to look like
the original, but produced by a means different from the original. |
| In this sense, a painting of a landscape is a forgery: applying paint to a canvas is
a different process from the geological, meteorological, and biological forces
that scuplt a landscape. |
| Yet when we begin to comtemplate virtual environments,
paintings and their scanned digital incarnations are too information-rich for
real time immersion. |
| To be sure, landscape images generated by fractal
and multifractal algorithms do not model the forces producing physical
landscapes. |
| However, real landscapes exhibit a scale-invariance (presumably,
the result of the same forces being applied over many lengths) fundamental
to fractal algorithms. |
| Consequently, we might expect fractals can be used
to produce a brief description of a realistic landscape. With the investment
of considerable cleverness by many people, this expectation is fulfilled. |
| So far, the production of fractal landscapes falls into three eras: |
| the heroic landscapes of Sig Handelman, |
the classical landscapes of Richard Voss, and |
the romantic landscapes of Ken Musgrave. |
|
| In the very first offering of a fractal geometry course at Yale
(spring semester, 1993), Musgrave
gave a guest lecture and presented a slide show of his landscape forgeries.
These are some examples. Click each picture to magnify.
|
|
| The class was appropriately impressed. After
Musgrave left, one student asserted a real picture had been included among those that
were computer-generated. Despite contradictory comments by the teacher,
several other students spoke up in agreement. There seemed little hope of convincing
them of their error, until it became clear that different students thought different
slides were real scenes. (None were.) This was one of the most lively discussions in the
semester. The students were genuinely shaken by their inability to distinguish
real from artificial. That these images were made with a modest amount of
information (arranged in an exceedingly clever way, to be sure) is among the
strongest evidence so far that fractals are a natural language for describing the
world around us. |
| That a cleverly designed fractal approach can give compact
encodings of scenes with great natural complexity suggests some aspect of the
fractal method does indeed model part of the natural process. |
| Just getting the
picture to look right is not enough, but if the picture can be described by a
small data set, we may have discovered an important organizing principle of the
subject of the picture. Yet again, fractals are revealed as a powerful way of
organizing our views of the world. |
