Getting Acquainted with Fractals Ebook

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The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia He wondered what a complex polynomial function would look like such as the ones named after him in the form of z2 c where c is a complex constant with real and imaginary parts The idea behind this formula is that one takes the x and y coordinates of a point z and plug them into z in the form of x iy where i is the square root of -1 square this number and then add c a constant Then plug the resulting pair of real and imaginary numbers back into z run the operation again and keep doing that until the result is greater than some number The number of times you have to run the equations to get out of an orbit not specified here can be assigned a colour and then the pixel xy gets turned that colour unless those coordinates cant get out of their orbit in which case they are made black Later it was Benoit Mandelbrot who used computers to produce fractals A basic property of fractals is that they contain a large degree of self similarity ie they usually contain little copies within the original and these copies also have infinite detail That means the more you zoom in on a fractal the more detail you get and this keeps going on forever and ever The well-written book Getting acquainted with fractals by Gilbert Helmberg provides a mathematically oriented introduction to fractals with a focus upon three types of fractals fractals of curves attractors for iterative function systems in the plane and Julia sets The presentation is on an undergraduate level with an ample presentation of the corresponding mathematical background eg linear algebra calculus algebra geometry topology measure theory and complex analysis The book contains over 170 color illustrationsGetting Acquainted with Fractals EbookBy Gilbert Helmberg Publisher De Gruyter Print ISBN 9783110190922 3110190923 eText ISBN 9783110206616 3110206617 Edition 1st Copyright year 2007 Format PDF Available from 18200 USD SKU 9783110206616

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9783110190922

The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia He wondered what a complex polynomial function would look like such as the ones named after him in the form of z2 c where c is a complex constant with real and imaginary parts The idea behind this formula is that one takes the x and y coordinates of a point z and plug them into z in the form of x iy where i is the square root of -1 square this number and then add c a constant Then plug the resulting pair of real and imaginary numbers back into z run the operation again and keep doing that until the result is greater than some number The number of times you have to run the equations to get out of an orbit not specified here can be assigned a colour and then the pixel xy gets turned that colour unless those coordinates cant get out of their orbit in which case they are made black Later it was Benoit Mandelbrot who used computers to produce fractals A basic property of fractals is that they contain a large degree of self similarity ie they usually contain little copies within the original and these copies also have infinite detail That means the more you zoom in on a fractal the more detail you get and this keeps going on forever and ever The well-written book Getting acquainted with fractals by Gilbert Helmberg provides a mathematically oriented introduction to fractals with a focus upon three types of fractals fractals of curves attractors for iterative function systems in the plane and Julia sets The presentation is on an undergraduate level with an ample presentation of the corresponding mathematical background eg linear algebra calculus algebra geometry topology measure theory and complex analysis The book contains over 170 color illustrationsGetting Acquainted with Fractals EbookBy Gilbert Helmberg Publisher De Gruyter Print ISBN 9783110190922 3110190923 eText ISBN 9783110206616 3110206617 Edition 1st Copyright year 2007 Format PDF Available from 18200 USD SKU 9783110206616