In mathematics, fractals are a self-similar subset of Euclidean space whose fractal dimensions strictly exceeds its topological dimension. So when you draw these functions in their topological height, fractals appear the same at different levels, as illustrated in successive magnifications of the Mandelbrot set.
Mandelbrot set is a good example to see how fractals are changing in every x,y and z planes. Drawing a Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive details at increasing zooming that makes the boundary of the Mandelbrot set as in fractal curves. The Mandelbrot set basically defined as a function of f(z)=z^2+c where z and c are complex numbers.
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In this post we want to show you how you can printout a Mandelbrot set in text form in C++ Builder. While we are able to draw as shown above in graphics we want to have fun with printing it in text form.
1.Create a new Multi-Device C++ Builder Console project, Save all unit and project files into a folder.
2. Let’s do as simple as possible. Clear all codes, add these library includes.
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#include <iostream> #include <complex> |
3. Now let’s create our own text_mandelbrot(…) function to draw a Mandelbrot set in text form as a console.
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void text_mandelbrot( int maxW, int maxH, int max_it) { for(auto y = 0; y < maxH; ++y) { for(auto x = 0; x < maxW; ++x) { std::complex<float> z,c = { 2.*x/maxW-1.5f, 2.*y/maxH-1}; int iteration = 0; while(abs(z) < 2 && ++iteration < max_it) z = z*z + c ; std::cout << (iteration == max_it ? 'O' : '.'); } std::cout << '\n'; } } |
As given in here we defined two complex numbers
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std::complex<float> z, c = { ... , ... }; |
We loop in row and column as x and y coordinates, and we calculate height of this function with complex numbers related with these row and column,
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z = z*z + c ; |
4. Finally we need to define our main function to run our text_mandelbrot(…) function.
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int main(void) { text_mandelbrot(78,22,20); getchar(); return 0; } |
5. Hit F9 to run your codes or run your code from Run button.
That’s all. This simple code compatible with most of C++ compilers, you may need few changes in some compilers. You can improve this code by drawing a part of this function (like zooming to a portion of it). Or you can use Bitmaps and directly draw it with full details. Don’t worry about calculations and speed about to draw these kind of functions in math. Because C++ is faster to calculate and draw these things. You can also use parallel programming methods to use all of your CPU and GPU cores draw anything multiple times faster.
Full Lines of VCL Console Application in C++ Builder should be like this;
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#include <vcl.h> #include <stdio.h> #include <iostream> #include <complex> void text_mandelbrot( int maxW, int maxH, int max_it) { for(auto y = 0; y < maxH; ++y) { for(auto x = 0; x < maxW; ++x) { std::complex<float> z,c = { 2.*x/maxW-1.5f, 2.*y/maxH-1}; int iteration = 0; while(abs(z) < 2 && ++iteration < max_it) z = z*z + c ; std::cout << (iteration == max_it ? 'O' : '.'); } std::cout << '\n'; } } int main(void) { text_mandelbrot(78,22,20); getchar(); return 0; } |
And the result will be like this;
Design. Code. Compile. Deploy.
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