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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

FITNESS. "Previous analyses of this experiment have shown numerous examples of parallel phenotypic and genetic evolution. All twelve populations underwent rapid improvement in fitness that decelerated over time." http://www.pnas.org/content/105/23/7899.full View in LinkedIn

NO CITRATE USERS. "In a long-term experiment, we propagated 12 populations of E. coli, all founded from the same ancestral strain, in a medium containing glucose, which is the limiting resource, and abundant citrate. For more than 30,000 generations, none of them evolved the capacity to use the citrate, although billions of mutations occurred in each population, such that any typical base pair mutation would have been tested many times in each one." http://www.pnas.org/content/105/23/7899.full View in LinkedIn

GENETIC COMPARTMENTALIZATION. "During evolution, the genomes of eukaryotic cells have undergone major restructuring to meet the new regulatory challenges associated with compartmentalization of the genetic material in the nucleus and the organelles acquired by endosymbiosis (mitochondria and plastids)." https://lnkd.in/d7Gtrg9 View in LinkedIn