Fractal landscapes in physics and biology

This article is based upon the Thirtieth Saha Memorial Lecture (delivered on 4 January 1992) and the Fourth Bose Memorial Lecture (delivered on 5 January 1992). I felt deeply touched to have been so honored by invitations to deliver these lectures, especially in view of the list of illustrious predecessors who have held this honor. At the outset I wish to acknowledge that almost all of my work is connected in one way or another to random walks, a topic about which I learned most from the classic 1943 review of the great Indian physicist S. Chandrasekar. I also wish to acknowledge my personal debt to the great culture and music of India, and to the many Indian scholars who have taught me their unique insights into the mysteries of physics. In particular, I wish to dedicate this work to the late Bengali genius Satyajit Ray, whose recent passing has left the world immeasurably poorer. It was my dream while in Calcutta to have the opportunity of meeting this hero of mine, but his ill health at that time prevented our meeting.