I spent my research time today in Magland's office, watching him explore the magic of the iterated maps I discussed yesterday. To recap: These are chaotic maps that do not optimize any scalar objective function (that we know) but which are attracted to fixed points that are related to (project to) solutions of the equations we want (phase retrieval with arbitrarily good data). We wondered how the author of these maps created them; we tried experiments in which we parameterized various choices and saw which maps work and which don't. We wondered about possible connections to MCMC, which is a stochastic iterated map (these are deterministic). The math is magical.
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