Mandelbrot Set is defined over the set of complex numbers. We can infinitely magnify some part of it and the same pattern will repeat over and over again. Koch Snowflake as shown in the image below: It meansĪ given object is similar (completely or to some extent) to some smaller part of itself. In mathematics, this phenomenon is known as self-similarity. We know very well that the left side matches exactly the right side, i.e. We can also compare different parts of the This notion is not only limited to a comparison of two different objects. We say two objects are similar to each other if they share We all have a common sense of the concept of similarity. In the second part, we will analyze one interesting property of the Julia Set. First, we will demonstrate the convergence of the Mandelbrot Set with anĮnticing animation. In this tutorial blog post, we will see how to construct fractals in Python and animate them using the amazing You crank the formulas several times andĪt the end, you get things like this (pointing to a stunning plot) One of the founding fathers of the fractal geometry said in his legendaryĪ surprising aspect is that the rules of this geometry are extremely short. The fractals may seem difficult to understand due to their peculiarity, but that's not the case. Strange geometry exhibits the same or similar patterns irrespectively of the scale. It may sound bizarre but the mathematicalĬoncept of fractals opens the realm towards this intricating infinity. Imagine zooming an image over and over and never go out of finer details. Animate Your Own Fractals in Python with Matplotlib
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Multiple game modes provide a stimulating orgy of objectives: penetrate and be penetrated as fast as possible or compete in absurd, silly and sexually suggestive games and challenges. Players control a detached penis complete with testicles and an anus. And with your help, that's exactly what he'll do.Ībout the GameGenital Jousting is an online and local multiplayer party game about flaccid penises and wiggly anuses for up to eight players at once. He wants to show everyone his astounding rigidity. Play as John, a dick who wants to find a date for his high school reunion. 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The English translation is, so far it looks like sunscreens with nanoparticles do stay on the surface of the skin where they should be.Īll in all, Titanium Dioxide is a famous sunscreen agent and for good reason, it gives broad spectrum UV protection (best at UVB and UVA II), it's highly stable, and it has a good safety profile. A 2009 review article about the safety of nanoparticles summarizes this, "to date, in-vivo and in-vitro studies have not demonstrated percutaneous penetration of nanosized particles in titanium dioxide and zinc oxide sunscreens". But do not panic, these are concerns under investigation. Once absorbed they might form unwanted complexes with proteins and they might promote the formation of evil free radicals. The main concern with nanoparticles is that they are so tiny that they are absorbed into the skin more than we want them (ideally sunscreen should remain on the surface of the skin). The itsy-bitsy Nano-sized particles improve both spreadability and reduce the whitish tint a lot, but unfortunately, it also introduces new health concerns. The cosmetic industry is, of course, really trying to solve this problem and the best solution so far is using nanoparticles. Sunscreens containing Titanium Dioxide are often hard to spread on the skin and they leave a disturbing whitish tint. The disadvantage of Titanium Dioxide is that it's not cosmetically elegant, meaning it's a white, "unspreadable" mess. Regular sized Titanium Dioxide also has a great safety profile, it's non-irritating and is pretty much free from any health concerns (like estrogenic effect worries with some chemical filters). Its protection is very good between 290 - 350 nm (UVB and UVA II range), and less good at 350-400 nm (UVA I) range. Methylene Bis-Benzotriazolyl Tetramethylbutylphenol (Nano)īis-Ethylhexyloxyphenol Methoxyphenyl Triazineĭiethylamino Hydroxybenzoyl Hexyl BenzoateĪnyway, it doesn't matter if it reflects or absorbs, Titanium Dioxide is a pretty awesome sunscreen agent for two main reasons: it gives a nice broad spectrum coverage and it's highly stable. |