Modern Algorithmic Aesthetics and Mathematical Harmony Throughout History

Fig. 0. Pythagoras Monochord (Rameau follows the scientific method of Galileo and Descartes).

Source: Robert Fludd, URL: https:// fineartamerica.com/shop/prints/robertþfludd

Fig. 1. The eight dots in the figure square connected with a closed line. Fig. 2. The program starts anywhere and drew an alternating horizontal and vertical line - in the horizontal one randomly to the left or right, in the vertical one with 23 partial stretches of random length. Fig. 3 & 4. The program began in a corner in the rectangular frame, draws one alternately horizontally and vertically - in the horizontal one randomly to the left or right, in the running track of 4000 sections, each one randomly less than 15 mm long. Fig. 5. The program defined two narrow areas to surround the bars of the cross and drew 50 random stretches in each area. 6. In the rectangular frame, the program drew 60 parallels to each side of the rectangular frame.

Source: Bense, M., Walther, E., 1968. rot 19: “Computer-Grafik” (German). Stuttgart:Elisabeth Walther

Modern Algorithmic Aesthetics and Mathematical Harmony Throughout History

Nessreen Y. Ibrahim

Nowadays the world has become more and more complex, where mathematics and natural sciences go different ways, and many mathematicians have decided to limit their activity to the problems of pure mathematics (Stakhov, 2009). The American mathematician Morris Kline in his book “Mathematics: The Loss of Certainty” mentioned that researchers should return to nature and natural sciences, which were the original objectives of mathematics (Kline, 1980). But throughout history, there was resistance to the efforts to attempt to apply scientific methods and mathematics to Aesthetics. Mathematics as an abstract language that had been created or discovered to understand the physical world was always far from evaluating aesthetic phenomena. There were some efforts to make a bridge between Mathematics and Art, but these were just fuzzy attempts. However, in the late 1950s scientific works showed the ability to apply scientific procedures to understand aesthetics and art (Berleant, 1967). But that was just an action to understand how to produce art and how to critique. George David Birkhoff [1884e1944] the mathematician who was interested in his early life in music, formalized new structural aspects of aesthetic perception. Where, he emphasizes the importance of patterns and tones that play a great role in aesthetic perception (Douchova, 2016
). While discussing his teleology theory (Huntley, 1970), claims that beauty has existed, and esthetics has been evaluated through time history for a certain purpose. As hunger and thirst ensure our bodily survival, while sex drives for the survival of the race, and fear has survival value, the question here is for what purpose do esthetic faculty come for? Why do humans need these subliminal emotions? Psychologists describe emotions as activities of the unconscious mind, therefore aesthetic experience is the resuscitation of subliminal emotions, and beauty is the power to evoke these emotions. So, the question could be more holistic; whether the mathematical nature of reality is mental; constructed by our minds or it is the abstract formula that controls the universe? Evaluating aesthetics has always been a real subject to understand how feelings, happiness, and emotional existence form and generate in humans.

SOURcE: Ibrahim, N. Y. (2022) "Modern Algorithmic Aesthetics and Mathematical Harmony Throughout History," Journal of Art, Design and Music: Vol. 1 : Iss. 1 , Article 2. Available at: https://doi.org/10.55554/2785-9649.1003

Nature-inspired Algorithms and Arithmetic Aesthetics

Studying the brain, cognition, and visual system in humans that measure or quantify aesthetics and trying to imitate methods of human aesthetic measurements are great challenges. Mimicking these methods to create a well-designed product is also a challenge. Many possible aesthetic criteria and evaluation methods could be used to achieve beauty and harmony in design. The algorithmic design method presents a wide design space for designers to achieve their goals. the below fig. presents an example of an Algorithmic Design for creating a ‘Phyllotaxis Pattern’, an arithmetic form that would be difficult to model by using traditional design methods. Phyllotaxis geometry considers the ubiquity of the Fibonacci numbers in nature. The design criteria in the Fig used a visual algorithmic program and two simple pattern algorithms that are inspired by nature; the Voronoi diagram-based algorithm and the Fibonacci sequence algorithm. the samples below represent sequential points that are equally spaced in a coordinate system (XY plane) arranged according to related functions. The designs were created with an infinite number of patterns inspired by nature. As the samples were generated from a model inspired by the Fibonacci generative rule in nature. The algorithmic experiments are based on biomimetic reference; Phyllotaxis and had been adapted and reparametrized to generate alternative design solutions. Understanding the hierarchical level of harmony, studying the mathematical.

Fig: Parametric Generative designs Phyllotaxis by using two simple pattern algorithms that are inspired by nature; Voronoi diagram-based algorithm and the Fibonacci sequence algorithm. (Visual algorithmic programs; Rhinoceros/Grasshopper). Source: Naturally Generative Algorithmic Designs by Nessreen Y. Ibrahim (Author).

SOURcE: Ibrahim, N. Y. (2022) "Modern Algorithmic Aesthetics and Mathematical Harmony Throughout History," Journal of Art, Design and Music: Vol. 1 : Iss. 1 , Article 2. Available at: https://doi.org/10.55554/2785-9649.1003