The Artistic Geometry of Consensus Protocols

The use of geometric patterns in art has a long history. The geometric period of ancient Greek art (ca. 900–700BC) is characterized by the extensive use of geometric motifs, mainly on vase and amphorae painting. These decorative motifs (meanders, triangles, circles, etc.) extend horizontally in multiple bands about the vase circumference, and they exhibit central and translational symmetry [7, 18, 45]. Elaborate symmetric geometric patterns also appear extensively in Islamic art, largely due to their aniconic quality [10, 11]. Influenced by previous classical Greek, Roman, and Sasasian works, and fueled by the intellectual contributions of Islamic mathematicians, astronomers, and scientists of the time, Islamic artists created this unique new style, which is characterized by repeated combinations and duplications of simple geometric forms (such as circles and the squares), arranged in intricate, interlaced geometric ornamentations whose complexity is ever increasing, offering the possibility of infinite growth [15]. The exploration of infinity and symmetric growth has also been explored bymany subsequent artists. TheDutch graphic artistM. C. Escher (1898–1972) is most famous for his exploration of infinity and of his creations of