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SYMMETRY. "These distortions had to obey the three, four, or six-fold symmetry of the underlying pattern in order to preserve the tessellation. The effect can be both startling and beautiful." (Reminiscent of the six-fold symmetry of snowflakes). https://lnkd.in/d_HZ4K8 View in LinkedIn

DEFECTORS. "In the short term, defectors sabotaged the viability of the group; but these findings nevertheless show that transitions to higher orders of complexity are readily achievable, provide insights into the selective conditions, and facilitate experimental analysis of the evolution of individuality." http://www.nature.com/nature/journal/v425/n6953/abs/nature01906.html View in LinkedIn

TRANSITIONAL OBSERVATIONS. "The costs and benefits of cooperation, plus evolutionary susceptibility to defecting genotypes, were analysed to determine conformation to theory. Cooperation was costly to individuals, but beneficial to the group. Defecting genotypes evolved in populations founded by the cooperating type and were fitter in the presence of this type than in its absence." http://www.nature.com/nature/journal/v425/n6953/abs/nature01906.html View in LinkedIn

EXPERIMENTAL TRANSITION. "Here we describe an evolutionary transition that occurs in experimental populations of Pseudomonas fluorescens propagated in a spatially heterogeneous environment. Cooperating groups are formed by over-production of an adhesive polymer, which causes the interests of individuals to align with those of the group." http://www.nature.com/nature/journal/v425/n6953/abs/nature01906.html View in LinkedIn

TRANSITION FROM SINGLE CELLS. "Although there is much theory, there are few empirical studies." https://lnkd.in/dM8VCEC View in LinkedIn

SO ENDS this journey into the work of MC Escher. He was deeply inspired by the remarkable Moorish art from the ancient Great Mosque of Córdoba in Andalucía Spain: "In the Great Mosque of Córdoba strong geometric principles based on the harmonic subdivisions of a squared circle in which the alternate sides relate in 1:2 and the consecutive relate in 1:√2 proportions appear to underline its architectural planning." Penrose and others expanded on this with the mathematics of tiling. But only MCE went through that mathematical door into the scented garden beyond. https://lnkd.in/dVZh_Zu View in LinkedIn

SELF REFERENCE. "On a deeper level, self-reference is found in the way our worlds of perception reflect and intersect one another. We are each like a character in a book who is reading his or her own story, or like a picture of a mirror reflecting its own landscape. Many of Escher’s works exhibit this theme of intersecting worlds." https://lnkd.in/d_HZ4K8 View in LinkedIn

ARTIFICIAL INTELLIGENCE. "A central concept Escher captured is that of self-reference, which many believe lies near the heart of the enigma of consciousness—and the brain’s ability to process information in a way that no computer has yet mimicked successfully." https://lnkd.in/d_HZ4K8 View in LinkedIn

THE IMPOSSIBLE. "One of the most intriguing is based on an idea of the mathematician Roger Penrose’s—the impossible triangle. In this lithograph, Waterfall, two Penrose triangles have been combined into one impossible figure." https://lnkd.in/d_HZ4K8 View in LinkedIn

MIRAGE. "A third type of “impossible drawing” relies on the brain’s insistence upon using visual clues to construct a three-dimensional object from a two-dimensional representation, and Escher created many works which address this type of anomaly." https://lnkd.in/d_HZ4K8 View in LinkedIn