![]() ![]() Mathematics, physics and chemistry can explain patterns in nature at different levels and scales. The Hungarian biologist Aristid Lindenmayer and the French American mathematician Benoît Mandelbrot showed how the mathematics of fractals could create plant growth patterns. ![]() In the 20th century, the British mathematician Alan Turing predicted mechanisms of morphogenesis which give rise to patterns of spots and stripes. Scottish biologist D'Arcy Thompson pioneered the study of growth patterns in both plants and animals, showing that simple equations could explain spiral growth. The German biologist and artist Ernst Haeckel painted hundreds of marine organisms to emphasise their symmetry. In the 19th century, the Belgian physicist Joseph Plateau examined soap films, leading him to formulate the concept of a minimal surface. The modern understanding of visible patterns developed gradually over time. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. These patterns recur in different contexts and can sometimes be modelled mathematically. Patterns in nature are visible regularities of form found in the natural world. Patterns of the veiled chameleon, Chamaeleo calyptratus, provide camouflage and signal mood as well as breeding condition. The crescent shaped dunes and the ripples on their surfaces repeat wherever there are suitable conditions. ![]() Natural patterns form as wind blows sand in the dunes of the Namib Desert. Furthermore, it is worth mentioning that it was not on this side of the globe that the Fibonacci sequence was written for the first time, it had already appeared in a book on metrics written by the Indian mathematician Pingala, between 450 and 200 BC, demonstrating that the sources of beauty and wisdom go beyond the European cradle.Visible regularity of form found in the natural world However, it is a fact that the golden ratio was of fundamental importance for the cultural sector and in the construction of an aesthetic sense, especially in the West. In short, it is a debate that will remain constant, after all, scientific data are not enough to translate what is beautiful - this notion being subjective and created according to a person's own references and cultures. According to Keith Devlin, a British mathematician and expert on the subject, all theories that cover aesthetic appeals according to this constant exist only because we humans are good at recognizing patterns and we ignore everything that contradicts them. Furthermore, many mathematicians and designers already question the fact that the golden ratio is a universal formula for aesthetic beauty. Nowadays, fortunately, the discussion about the standardization and universalization of the human body is much more advanced and does not just surrender to mathematical factors. The higher the numbers chosen, the closer the result is to the golden ratio. After all, when dividing a number from the Fibonacci sequence by its previous one, the result will be closer and closer to 1.618. This constant creates a very close relationship with the golden number (1.61803399), called the golden ratio, which mathematically represents the "perfection of nature". In its content, the fundamental thing is to know that whatever the number in the sequence is, it is the result of the sum of the two previous ones. Leonardo of Pisa, better known as Fibonacci, wrote his series of numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.) to solve a hypothetical problem of breeding rabbits in your Calculation Book. But, after all, how does this sequence relate to architecture? ![]() The famous sequence of numbers became known as the "secret code of nature" and can be seen in the natural world in several cases. One of the most famous series of numbers in history, the Fibonacci sequence was published by Leonardo of Pisa in 1202 in the " Liber Abaci", the "Book of Calculus". ![]()
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