Mandelbrot Sets, Fractals, Dynamical Systems, Mathematics, Physics, Arts by Rendering, Cryptography, Astrophotography and Spirituality – A Connecting Post

Introduction All fractals can be generated using an Iterated Function System (IFS). An IFS consists of a function f which is executed in a feedback loop, also known to computer students as a recursive function. That means, the output of the function is given as input when the function calls itself. The first time the …

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Mandelbrot Set, Dynamical Systems, Mathematics, Physics, Arts by Rendering, Cryptography and Spirituality – Preface

Just before finishing enjoyable to write, lovely all encompassing post, some interest to ignite curiosity... Mandelbrot Set, Dynamical Systems, Mathematics, Physics, Arts by Rendering, Cryptography and Spirituality https://youtu.be/0jGaio87u3A A groundbreaking record in the numbet of itterations in a Mandelbrot Set https://youtu.be/FFftmWSzgmk Mandelbrot Set Explained https://youtu.be/apP1Q7v6M7Y The Buddhabrot Technique Explaned (by Melinda Green) The Dynamicsl Approach …

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Routes to Chaos: The Non-Linear Dynamical System Approach and Lorenz Equations – Part II

If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment - Henri Poincaré In "Routes to Chaos: The Non-Linear Dynamical System Approach – Part I" we gave a short introduction of the subject, …

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Vorticity and Coherent Structures – Part I

“Big whorls have little whorls that feed on their velocity, and little whorls have lesser whorls and so on to viscosity” – Lewis Fry Richardson Introduction Although this post shall take great advantage of the notion of vorticity to get a glimpse on the small scale organized fluid elements of significant life-time and scale we call …

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Transition to Turbulence Series – Transition Scenarios

Motivation: There are various type of instabilities for a number of flow patterns. The intention of this post is to investigate how these instabilities may trigger laminar-turbulent transition. I shall do my best to classify these routes leading from a stable laminar to a disturbed one flow, and base my path on the mechanisms responsible …

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