Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality (D), symmetry, recursion, and the number of segments in the generator using a variety of fractal patterns. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as D increases. For the majority of individuals, preference increased with D. We replicated these results in a second study, while also testing the effects of symmetry and recursion by presenting fractals without mirror symmetry (asymmetric dragon fractals and radially symmetric dragon fractals) and fractals with mirror symmetry (Sierpinski carpets and Koch snowflakes). We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in asymmetric patterns, while others were less discriminating. Here, what distinguished among respondents was their sensitivity to the presence of mirror symmetry. All participants in the second study exhibited a general increase of preference with D. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a pattern. Conceptualizations such as Berlyne’s (1971) and Redies’ (2015) theories of aesthetics provide a suitable framework for interpretation of our data with respect to the individual differences that we detect. Future studies that incorporate physiological methods to measure the human aesthetic response to exact fractal patterns would further elucidate our responses to such timeless patterns.

/pdf/aesthetic-responses-to-exact-fractals-driven-by-physical-45gd6e86pp.pdf

Aesthetic Responses to Exact Fractals Driven by Physical Complexity.

With a severe energy crisis facing the modern world, the production and utilization of ener‐ gy has become a vital issue, and the conservation of energy has acquired prime importance. Energy production and consumption are directly related to everyday life in much of human society, and issues of energy research are extremely important and highly sensitive. Being aware of the global warming problem, humans tend to rely more on renewable energy (RE) resources.

/pdf/wind-turbine-power-the-betz-limit-and-beyond-2264s57opc.pdf

Wind Turbine Power: The Betz Limit and Beyond

Geographic space demonstrates scaling or hierarchy, implying that there are far more small things than large ones. The scaling pattern of geographic space, if visualized properly (i.e., based on the head/tail breaks classification), can evoke a sense of beauty. This is our central argument. This beauty is a new type of aesthetic at a deeper structural level and differs in essence from an intuitive sense of harmony, perceived in terms of color, shape, texture, and ratio. This new kind of beauty was initially defined and discovered by Christopher Alexander, and promoted in his master work The Nature of Order. To paraphrase Mandelbrot, this is beauty for the sake of science rather than for art's sake or for the sake of commerce. Throughout the article, we attempt to argue and illustrate that the scaling of geographic space possesses this new kind of beauty, which has a positive impact on human well-being. The article further draws on the previous work of Nikos Salingaros and Richard Taylor on the beauty in a...

A New Kind of Beauty Out of the Underlying Scaling of Geographic Space

Does systolic and diastolic blood pressure follow Golden Ratio

Golden ratio: A subtle regulator in our body and cardiovascular system?

Sir, in the article on perceived aesthetics of maxillary incisors1 no mention was made of the Golden Ratio. This is a ratio 1.61:1 and is also referred to as the Divine Number. It has been known for over 2,500 years. It occurs in nature and science and has been used in architecture; reputedly the Parthenon was built to these proportions. There are claims of its use by artists such as Dali. Many psychologists have carried out tests presenting a range of rectangular shapes to subjects. There is a consistent finding that the most pleasing shape conforms to the Golden Ratio. P. Erridge East Grinstead

The golden ratio.

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The golden ratio.