| Strange attractors have detailed structure on all scales of magnification and were one of the early fractals to be studied. |
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| For example, we observe the presence of coexisting lipid phases and unstable domain growth that results in patterns such as fractals. |
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| Some of the complexity has been captured in modern pictures of fractals, many of which are created by iterating functions of this kind. |
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| He showed how fractals can occur in many different places in both mathematics and elsewhere in nature. |
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| The approach of this paper was originally developed in to study the Hausdorff measure of certain parameterized families of fractals. |
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| Mathematicians have long been taken with the concept of fractals, which posits that patterns are made up of smaller, self-contained patterns. |
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| Many natural chaotic systems form fractals in the patterns that record the process. |
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| Of course, no class on maths and the visual arts would be complete without fractals. |
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| He noted that the body is full of fractals, self-similar repeating patterns at different scales, just as nature is full of fractals. |
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| This requires fractals to be given dimensions that are not whole numbers but fractions. |
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| All of these elements are combined into seemingly aleatory compositions that, like fractals, operate on several scales at once. |
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| Mathematicians can use similar algorithms to generate fractals and other forms. |
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| Topics ranged from the golden mean, spirals, and tessellations to fractals, origami, and impressionist art. |
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| You can find an amazing repository of examples including all the most famous fractals such as Serpinski's triangle or Koch triadic Island. |
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| This much is clear from so-called fractals, which have become the iconic face of the chaos concept. |
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| If you're addicted to science books, pick up this short and eminently readable book and enjoy the bizarre tale of fractals and strange attractors. |
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| Computer programs help diagram elaborate formations of tiny spirals that form massive, spiraled fractals to describe, say, the economic tendencies of your new, island society. |
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| Google's celebrating Gaston Julia, which means fractals agogo. |
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| The implications of map theory, game theory, topology, the fractals of chaos theory, have all lurked in ornament, awaiting their elevation to science. |
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| Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals, and other ideas furnished the mathematical underpinnings. |
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| Another part of us recognizes instinctively that nature designs in fractals, with intriguing detail on every scale from the microscopic to the macroscopic. |
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| This property is the principal characteristic of fractals within chaos theory. |
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| The reverse also applies: Trees, coastlines, cauliflowers and snowflakes can all be considered natural fractals. |
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| If I buy my computer to send email with, and I want to make fractals, I don't have to buy a new fractal machine. |
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| The paths of synthesis are like crystal structures, like fractals, and they repeat themselves from the bigger ones to the smaller ones. |
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| Like a mountain range whose profile appears equally craggy when observed from both far and near, fractals are used to define curves and surfaces, independent of their scale. |
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| It is an original mixing between deterministic and non deterministic fractals. |
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| Using the unique space-filling and multi-level properties of fractals, Fractus is shaping the future of antennas with its significant intellectual property portfolio of 42 patent families. |
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| Yet it is striking the extent to which countries that took intelligence seriously during the Cold War face fractals of the same challenge-whether those countries are former neutrals, NATO allies or former enemies. |
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| Having defined the necessary tools for studying fractal structures, it is now time to get to the heart of the matter by giving the first concrete examples of fractals. |
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| Many of the fractals created in this way look astonishingly natural, which is why computer graphic artists use the convenient formulas of chaos theoreticians to depict mountain landscapes, for example. |
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| Apophysis is a freeware which lets you generate and edit flame fractals. |
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| The patrons of the Xplora portal are Professor Benoit Mandelbrot, the eminent mathematician who discovered fractals and Ray Kurzweill, a leading expert in artificial intelligence. |
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| They are related to fractals, in that they have self-similar patterns. |
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