Figure 1a. The Mandelbrot set illustrates self-similarity. As the image is enlarged, the same pattern re-appears so that it is virtually impossible to determine the scale being examined. Figure 1b. The same fractal magnified six times. Figure 1c. Figure 1d. Fractals are distinguished from regular geometric figures by their fractal dimensional scaling. As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve can be conceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.:48:15 There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. Introduction The word "fractal" often has different connotations for laypeople than mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception. History Figure 2.
Related: philosophy tree
• Complex Systems
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