I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.

In order to turn natural history into a true science, one would have to devote oneself to investigations capable of telling us not the particular shape of such and such an animal, but the general procedures of nature in the animal's production and preservation. 'Lettre sur le progress des sciences' in Oeuvres de Mr. De Maupertuis (1756), Vol. 2, 386.

Of what use are the great number of petrifactions, of different species, shape and form which are dug up by naturalists? Perhaps the collection of such specimens is sheer vanity and inquisitiveness. I do not presume to say; but we find in our mountains the rarest animals, shells, mussels, and corals embalmed in stone, as it were, living specimens of which are now being sought in vain throughout Europe. These stones alone whisper in the midst of general silence.

The poet's eye, in a frenzy rolling,
Doth glance from heaven to earth, from earth to heaven;
And as imagination bodies forth
The forms of things unknown, the poet's pen
Turns them into shapes, and gives to airy nothing
A local habitation and a name.

Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. 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... Nature exhibits not simply a higher degree but an altogether different level of complexity.