Vorticity map, partial derivatives equation, turbulence

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1 year ago

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$Fractal Art, as the name says, is fractals made art. Its is not drawn or painted by hand (traditional or digital). It is created with fractal generating software (for example, Apophysis, Mandelbulb 3d, Ultra Fractal, and many others), in roughly two step: defining the parameters for a set of selected functions, and rendering it into actual artwork. Although some fractals also may incorporate non fractal images, certain photomanipulation techniques (particulary plugins similar to fractalius or ka$

Local and global approaches in mathematics and machine learning are both universal approximators, but they differ in the number of parameters required to represent a given function accurately. The entire system, including data, architecture, and loss function, must be considered, as they are interconnected. Data can be noisy or biased, architecture may demand excessive parameters, and the chosen loss function may not align with the desired goal. To address these challenges, practitioners should

By examining the modulus of continuity, mathematicians can analyze the convergence, differentiability, and continuity of functions and sequences. It helps us understand the smoothness properties on both local and global scales, shedding light on the intricate relationships between local fluctuations and global patterns. In the realm of analysis, the modulus of continuity plays a fundamental role in studying functions' properties, such as Lipschitz continuity, Hölder continuity, or even different

In a place where no one ever came close to dreaming about... a place from a foaming brain, there is a tiny ripple of truth that duplicates sanity to reality... existence of self-pity and triumph! This is a long gone dream in which only lost souls find mercy from a god of an insane creation! Blowing cold winds that come from an uneven breathing pattern warm the frigid core of the sun! Rotting brain from inside the brittle bone of an old branch impatiently waiting to outgrow the sky… You are lost

[Ultra Fractal art] Deux heures moins le quart avant Jésus-Christ, by Jean Yanne

So, my fellow seekers of mathematical truth, let us don our mathematical finery and embrace the duality of global and local. With the modulus of continuity as our guide, we shall unravel the secrets hidden within the curves and functions. With each step, we shall uncover the delicate balance between the minute details and the sweeping vistas, all while basking in the radiance of mathematical style.[Liwa Dunes] .The interplay between the local and the global is a mathematical elegance. The loca

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