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What is the usage of mandelbrot set and julia set in programming? Is there any sample competitive problems that use these set?
To the best of my knowledge, the Mandelbrot set (and Julia set alike) is computed to produce beautiful fractal pictures and animations, and there aren't any other good reasons to compute it.
Designing algorithms to compute Mandelbrot efficiently requires skills in complex analysis, bigint arithmetic, and low-level assembly code optimization.
Using Mandelbrot for competitive problems would be problematic due to floating-point round-off errors, which can make it hard to compare results and tell which one is correct. Though depending on what you mean by competitive, you could consider that making Mandelbrot deep zoom videos to be competitive (with bigger and bigger magnification factors) - you can see YouTube for examples.
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I'm researching on compression algorithms (huffman coding and LZ77) and was wondering how I would evaluate their efficiency depending on the input image. I know how they work but I can't find information on their evaluation (mathematically). Thanks!
General-purpose (universal) compressors like LZ77 are usually compared by testing them against a standard set of sources and comparing the results, see: http://www.maximumcompression.com/, http://www.maximumcompression.com/data/summary_mf.php, for example.
Compressors for specific purposes are tested against source sets that are chosen to be as representative as possible.
For some applications it is also useful to place mathematical bounds on compression efficiency in terms of the source entropy.
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Does anybody know the examples of indefinite or definite integral that can be done in the terms of elementary functions manually by a good first-year or second-year student, but which Wolfram Alpha (or Mathematica) evaluate not correctly?
In other words, I want to find some tasks for mathematical test, where students cannot easily find the answer using wolfram and just rewrite it in their papers.
Thanks in advance.
It is probably impossible. Set of functions known by 1-2 years students is constrained. Mathematica uses symbolic algebra system to transform integrals, and big repository with properties of functions.
http://functions.wolfram.com/
For example for Hypergeometric Functions you have (218,254 formulas)!
Methods of calculations of integrals are explained on wolframalpha.com as step by step solutions for pro users. ($4.75/mo billed annually or $6 billed monthly)
Calculating integrals by computers is nowadays on level comparable to chess games. You have to talk with student individually.
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Lets say that my definition of 'rudimentary programming' refers to the fundamental tools employed for a computer to perform a task.
Considering programming rudiments, the learning spectrum usually looks something like this:
Variables, data types and variable memory
Arrays/Lists and their manipulation
Looping and conditionals
Functions
Classes
Multi threading/processing
Streams (hard-disk and web)
My question is, have I missed any of the major rudiments? Is there a 'next' to the spectrum that still eludes me?
I think you missed the most important one: algorithms. Understanding the complexity, know the situation to use them, why use them and more important, how to implement them.
I'm pretty sure that you already know a lot about algorithms but if you think that your tool-knowledge (aka the programming languages) are good enough, you should start focus, more, on the algorithms.
A great book to start is: Introduction to Algorithms, from Thomas H. Cormen
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I'm very impressed to how plagiarism checkers (such as Turnitin website ) works. But how do they do that ? In a very effective way, I'm new to this area thus is there any word matching algorithm or anything that is similar to that is used for detecting alike sentences?
Thank you very much.
I'm sure many real-world plagiarism detection systems use more sophisticated schemes, but the general class of problem of detecting how far apart two things are is called the edit distance. That link includes links to many common algorithms used for this purpose. The gist is effectively answering the question "How many edits must I perform to turn one input into the other?". The challenge for real-world systems is performing this across a large corpus in an efficient manner. A related problem is the longest common subsequence, which might also be useful for such schemes to identify passages that are copied verbatim.
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Does any have an algorithm for creating infinite terrain/landscape/surface?
Constraints
The algorithm should start by a random seed
The algorithm should be one to one, (the same seed gives the same result)
Other input parameter are allowed as long as 2 is fulfilled
The algorithm may output a 2d map
It suppose to create only surface with varying height (mountains), not three, ocean etc.
I’m looking for an algorithm and not a software.
It should be fast
None of other related questions in here answers this question.
If anything is unclear please let me know!
I would suggest something like Perlin noise, I've used it before for something like you're describing above, and it fits the bill. Check out this Example and you can see the sort of output you would expect from the noise generator.Here is a link to algorithm p-code too.
http://freespace.virgin.net/hugo.elias/models/m_perlin.htm
As others already said perlin noise is a possibility. Gpugems 3 has a nice capter about procedual generation using (IIRC, it has been some time since I read this) 3D Perlin noise.
Of course there are other methods too, e.g. Vterrain.org might be worth a look.