## Fractal Worlds: Grown, Built, and ImaginedFractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame--a close collaborator with Benoit Mandelbrot, the founder of fractal geometry--and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology. Frame and Urry offer new insights into such familiar topics as measuring fractal complexity by dimension and the life and work of Mandelbrot. In addition, they delve into less-known areas: fractals with memory, the Mandelbrot set in four dimensions, fractals in literature, and more. An inviting introduction to an enthralling subject, this comprehensive volume is ideal for learning and teaching. |

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### Contents

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### Common terms and phrases

2-cycle applied Benoit bins box-counting dimension boxes of side branch Brownian motion calculation Cantor set cardioid chaos chaotic circle inversion clusters coastline complex number complicated compute converge copies scaled corresponding cube cycle disc distribution driven IFS points dynamics earthquakes eigenvalues example exponent Figure fixed point forbidden pairs fractal antennas fractal dimension fractal geometry function galaxies gives Hausdorff dimension image of Fig infinity Internet interval iterates Julia set Koch curve line segment logistic map look lungs magnification Main cardioid Mandelbrot set math mathematical matrix measure multifractals networks Newton’s method older author patterns Phys picture pieces scaled power law produce driven random fractal refers to Sect regime rules scaled by 1/2 scaling factors second image self-affine self-similarity sequence shape side length Sierpinski gasket smaller solution space square story structure theorem tion transformations transition graph values vertices