V
F orew ord
To Frédéric (Frédo) Poupaud, who inspired my mind and soul.
… They are going to look for the highest dune so they can
see all the Sahara. They walk a long time. Outka says: ‘I see
a high dune’, and they go to it and climb up to the top. Then
Mimouna says: ‘I see a dune over there. It’s much higher and
we can see all the way to In Salah from it.’ So they go to it
and it is much higher. But when they go to the top, Aicha
says: ‘Look! There’s the highest dune of all. We can see to
Tamanrasset.’ …
(Paul Bowles, The Sheltering Sky, 1911)
The project for this book started in the beginning of the year 2005, when I looked
through some of my photographs taken in various parts of the world over the
last ten years or so. In fact, I have been interested and active in photography for
some decades and my pleasure in it has even increased exponentially since the
rise of digital imaging
1
. It then happened that I started to look at some of my
images in mathematical terms, more precisely, I started to see partial differential
equations ‘behind’ certain images. For example, a waterfall is modeled by the
Saint-Venant approximation of the Euler or Navier–Stokes equations, flows of
and in sand dunes obey the laws of the granular material inelastic Boltzmann
equation, patterns in animal skins are described by an instability phenomenon
in reaction-diffusion equations … All this has been clear to me for a long time,
but all of a sudden the idea came up to use photography as a vehicle to transport
and convey ‘my’ mathematics.
So the generic connection between my two favorite subjects, applied partial
differential equations and photography was found …
Actually, this is precisely what this book is all about. Topics in applied partial
differential equations are described mathematically in non-specialistic terms
tomakethebookaccessibletoalargeaudience–hopefullyalsogettingyoung
researchersinterestedinthesubject–andthesetopicsareillustratedby(as
I like to think) beautiful photographs, taken by myself in the last few years
(there are two exemptions, which were taken by Andrea Baczynski). All the
1
see my image galleries at www.pbase.com/markowich
