The coastline measured on a large scale map was approximately half the length of. Those people were British cartographers, who encountered the problem in measuring the length of Britain coast. Mark Pollicott, Lectures on Fractals and Dimension Theory, April-May 2005, 106 pages.ĭavid Worth, Construction of Geometric Outer-Measures and Dimension Theory, MS Thesis (University of New Mexico), December 2006, xi + 77 pages. Although fractal geometry is closely connected with computer techniques, some people had worked on fractals long before the invention of computers. In other words, the surface resulting from the procedure is not a deterministic, but rather a random surface that exhibits fractal behavior. I haven't looked for this material on the internet in several years, so there are probably other such items I don't know about that are worth looking at. A fractal landscape or fractal surface is generated using a stochastic algorithm designed to produce fractal behavior that mimics the appearance of natural terrain. On the other hand, you won't see Julia sets or coastlines or the word "fractal" in Rogers' book (except in the 21 page and 94 item bibliography Forward by Falconer in the 2nd edition of the book).Īlso, below are a couple of nice treatments I posted in sci.math about 5 years ago that I think are definitely worth looking at. onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth. Rogers Hausdorff Measures (if you're more interested in general metric space considerations) or Mattila's Geometry of Sets and Measures in Euclidean Spaces (if you're more interested in geometric measure theory in $^n$ come into play), and he deals with Hausdorff measures for general measure functions and not just for power functions. Affordable digital textbook from RedShelf: Fractal Geometry by: Kenneth. If you're mainly interested in a pure mathematics perspective, I suggest beginning with Falconer's The Geometry of Fractal Sets and then going to C. Since the 1980s fractals have attracted widespread interest. There are several ways to proceed, depending on your background and interests. Mandelbrot introduced the word fractal as a general description for a large class of irregular objects, and highlighted the need for a fractal mathematics to be developed, or in some cases retrieved from isolated forgotten papers. This is an slightly edited and expanded version of my comment.
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