Abstract
A prototype model is introduced for self-replicating octahedral shell structures. The structure is inherently aperiodic and unable to grow like a normal crystal. Conditions under which this growth mechanism may become favored energetically are discussed. High-resolution electron microscope images of the clay mineral allophane, an analog of the spheroidal fullerenes, are described. Kinetic equations are derived assuming an autocatalytic self-replicating growth mechanism for this model. More general mathematical treatments of self-replicating systems are also reviewed and discussed.
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