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 + i*y,
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 (x,y) gets turned that colour,
unless those coordinates can't 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, i.e., 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, e.g., linear algebra, calculus,
algebra, geometry, topology, measure theory and complex analysis. The
book contains over 170 color illustrations.
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Produktdetaljer
ISBN
9783110206616
Publisert
2015
Utgave
1. utgave
Utgiver
Vendor
De Gruyter
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter