what is the application of fractal geometry in computer?

Answer 1

As far as using fractals to design one, I can think of none. You can graph fractals using a computer and get some fascinating art.

Answer 2

Having background both in engineering (undergrad-level) and in mathematics (undergrad and grad-level), I'd have to say that measure theory is more something that formalizes a lot of what you *think* you can do. You can really think of measure theory as having one practical output: a well-defined, nicely-behaved theory of integration that allows us to do all of the operations we'd like to without worrying too much about details. Measure theory doesn't appear to have any practical uses because in undergraduate courses in most subjects the professor just waves their hands at any point that it really needs to be invoked (such as when you take limits of integrals). Here are some examples: Anything involving Fourier transforms, for example, really requires measure theory to do correctly (both in selecting the correct abstract setting for the problem and in the mechanics of evaluating the transform). If you have any familiarity with electrical engineering or physics, you'll know that the dirac delta abounds. This is a concept that can again be formalized properly using measure theory (or using the theory of distributions, which in turn requires measure theory in its definition). Of course, the other huge branch of mathematics where it is used is probability theory. If you go dig out a probability book, you'll really see that all you're talking about are particularly well-behaved measures. Any grad-level probability course is taught using the language of measure theory. Again, the undergrad treatment essentially just treats anything that needs to be justified using measure theory as an axiom. Some concepts that are very important for practical modelling such as ergodicity require measure theory to even be defined. If you want to go even more applied, many modern image processing problems are phrased in terms of geometric measure theory. Whether this approach is as practical as you'd like it to be is somewhat debatable, but it is in use. Anyway, I guess in the end it is debatable: are these really practical applications of measure theory? One way of thinking of it is this way: just because a discipline is somewhat esoteric right now does not mean that it should not be more well-known. I think in some of the sciences there is a dangerous assumption that everything in the world can be modelled completely correctly using mathematics gleaned from first and second-year math courses. A lot of the time if you go through the details correctly, you'll see that what you want to be true is not so obvious.

Answer 3

computers live on maths and logic. Anything that can be expressed mathematically, can be processed by computers.