1977*The Fractal Geometry of Nature*.*Fractals in Geophysics*. 1989, with Christopher H. Scholz*Fractals and Chaos*. 20042004, with Richard L. Hudson*The (Mis)Behaviour of Markets*.

- Forward: People and events behind the
*Science of Fractal Images*. 1988. (In*The Science of Fractal Images*) - Fractal landscapes without creases and with rivers. 1988. (In
*The Science of Fractal Images*) - Fractals -- a geometry of nature. 1992. (In
*The New Scientist Guide to Chaos*)

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.

The classic view of market behaviour is Gaussian, memoryless changes to
prices: random walks. This leads to a very low probability of large
changes. But we've experienced several crashes: real markets seem more
turbulent. Mandelbrot discusses these issues, and says that the evidence
demonstrates that real market behaviour follows "fat tailed"
power laws, with long term memory: they have a fractal structure. Such
behaviour has a *much* higher chance (many many many orders of
magnitude) of large fluctuations (so, "million to one chances happen
nine times out of ten"). So the classic theory gives an *extremely*
skewed view of risk, and people can lose lots of money.

Mandelbrot agrees that his own multifractal theory of market prices,
started in the 60s and gradually refined over the decades, is not yet
finalised, but that nevertheless it is a much better fit to observations
than the classic theory. He argues extremely strongly, and compellingly,
for a proper *science* of finance: it is too important to be left to
guesswork, intuition, and outmoded theories. His theory might not help you
make money, but it could stop you losing it all in one big crash.

This is a fascinating book, very readable, with lots of food for thought.