Four interesting problems concerning Markovian shape sequences

In earlier work, we investigated the dynamics of shape when rectangles are split into two. Further exploration, into the more general issues of Markov ian sequences of rectangular shapes, has identified four particularly appea ling problems. These problems. which lead to interesting invariant distribu tions on [0,1], have motivating links with the classical works of Blaschke, Crofton, D. G. Kendall, Renyi and Sulanke. AMS 1991 Subject Classification : Primary 60D05 Secondary 60E05; 60J05.