Getting acquainted with fractals

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The first instance of pre-computer fractals was noted by French mathematician Gaston Julia, who explored complex polynomial functions, particularly those in the form of z² + c, where c is a complex constant. This formula involves taking the x and y coordinates of a point z, represented as x + i*y (with i as the square root of -1), squaring it, and adding c. This process is repeated until the result exceeds a certain threshold. The number of iterations required to escape a specified 'orbit' can be assigned a color, turning the pixel (x, y) that color, while those that remain trapped are colored black. Benoit Mandelbrot later utilized computers to generate fractals. A key characteristic of fractals is their self-similarity; they contain smaller copies of themselves with infinite detail. Zooming in reveals more intricate patterns indefinitely. Gilbert Helmberg's well-written book offers a mathematically oriented introduction to fractals, focusing on curves, attractors for iterative function systems, and Julia sets. It is aimed at an undergraduate audience and includes essential mathematical concepts such as linear algebra, calculus, geometry, and complex analysis, complemented by over 170 color illustrations.