Fractals everywhere
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The first half of this paper is the written version of the invited talk presented at Unconventional Computing UC10, The University of Tokyo, Japan, June 21---25, 2010. It describes some salient features of hypercomputation in Dickson algebras. Such quadratic algebras form an appropriate framework for nonlinear computations which does not limit a priori the computational power of multiplication. They underlie paradoxical mathematics whose potential interest to analyse some computational aspects of the human mind which resist the classical approach is presented. In its last part, the paper offers new glimpses on the organic logic for hypercomputation by developing a fresh look at plane geometry in relation with the 驴 function.