Video Infoblog: Walking city streets: Catalan Closed Form (visual proof from lattice paths)

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Human Consciousness of Fractals

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Human Consciousness of Fractals What are the intricacies involved in the human consciousness of fractals? The human consciousness of fractals involves the perception and interpretation of complex patterns and shapes that repeat on multiple scales. Fractals are often visually appealing to people, and they have been used in a variety of artistic, architectural, and scientific applications. In terms of perception, the human visual system is well-suited to recognizing fractal patterns. This is because fractals tend to have self-similar features that repeat on multiple scales, and the human visual system is adept at detecting patterns and recognizing similarities. This makes fractals a natural fit for human visual perception, and it is likely that our brains are wired to recognize and respond to fractals in certain ways. In terms of interpretation, people often associate fractals with concepts like chaos, unpredictability, and complexity. This is because fractals can be used to model comple...
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What is Hyperbolic Geometry?

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 Hyperbolic geometry is a type of non-Euclidean geometry that differs from classical Euclidean geometry in its treatment of parallel lines. In Euclidean geometry, parallel lines are equidistant and will never meet. In hyperbolic geometry, parallel lines can get arbitrarily close but will never intersect. Hyperbolic geometry is characterized by a constant negative curvature, meaning that lines curve away from each other, and objects in hyperbolic space appear to be "slimmer" than in Euclidean space. This leads to counterintuitive results, such as the fact that in hyperbolic geometry, there are more parallel lines to a given line through a point than there are in Euclidean geometry. Hyperbolic geometry has important applications in many areas of mathematics, including number theory, cryptography, and the study of Riemann surfaces. It is also used in physics to model the behavior of certain physical systems, such as the geometry of space-time in general relativity.
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The Beautiful Structure of Cosmic Nothingness: Understanding Immutability

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The Beautiful Structure of Cosmic Nothingness: Understanding Immutability. - https://medium.com/@najmanhussain/the-beautiful-structure-of-cosmic-nothingness-understanding-immutability-b54e7747da6b I hope that this write-up is appealing to the imagination. It is not intended to be rigorous.. Since time immemorial, humans have wondered what life on earth was all about. They would not have missed the fact that not all patterns are exhibited in the natural world. Only certain shapes are exhibited in the realm of nature and these are beautiful. In the last couple of decades, we have deepened our knowledge to include fractal geometry. “A fractal is a never-ending pattern..They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems..” What are Fractals? — https://fractalfoundation.org/resources/what-are-fractals/ I came across fractals only lately, well after I went into retirement. Briefly, fractals are...
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