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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This Mandelbrot_to_bitmap procedure directly draws Mandelbrot fractal to a bitmap in given iterations. In this example we try as simple as possible.
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void mandelbrot_to_bitmap( TBitmap *bmp, int max_iteration) { TBitmapData bitmapData; TAlphaColorRec spec[256]; for(auto i=0; i<256; i++){ spec[i].A=0xFF; spec[i].R=0; spec[i].G=0; spec[i].B=i; } if( bmp->Map(TMapAccess::ReadWrite, bitmapData)) // Lock bitmap and retrive bitmap data { for(auto y = 0; y < bmp->Height; ++y) { for(auto x = 0; x < bmp->Width; ++x) { std::complex<float> z,c ={ 2.*x/bmp->Width-1.5f, 2.*y/bmp->Height-1 }; int iteration = 0; while(abs(z) < 2 && ++iteration < max_iteration) z = z*z + c ; bitmapData.SetPixel(x, y, spec[iteration%255].Color); } } } bmp->Unmap(bitmapData); } |
In this post we want to draw a Mandelbrot set into Canvas of a Bitmap in C++ Builder. It is presented that Mandelbrot can be drawn in text form as in here (link***).
1.Create a new Multi-Device C++ Builder (FMX) project, Save all unit and project files into a folder.
2. Add a Button (TButton) and an Image (TImage) to show final bitmap.
3. Double click to Button and modify lines as below;
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#include <fmx.h> #include <complex> #pragma hdrstop #include "Mandelbrot_GFX_Unit1.h" //--------------------------------------------------------------------------- #pragma package(smart_init) #pragma resource "*.fmx" TForm1 *Form1; //--------------------------------------------------------------------------- __fastcall TForm1::TForm1(TComponent* Owner) : TForm(Owner) { } //--------------------------------------------------------------------------- void mandelbrot_to_bitmap( TBitmap *bmp, int max_iteration) { TBitmapData bitmapData; TAlphaColorRec spec[256]; for(auto i=0; i<256; i++){ spec[i].A=0xFF; spec[i].R=0; spec[i].G=i/2; spec[i].B=i; } if( bmp->Map(TMapAccess::ReadWrite, bitmapData)) // Lock bitmap and retrive bitmap data { for(auto y = 0; y < bmp->Height; ++y) { for(auto x = 0; x < bmp->Width; ++x) { std::complex<float> z,c ={ 2.*x/bmp->Width-1.5f, 2.*y/bmp->Height-1 }; int iteration = 0; while(abs(z) < 2 && ++iteration < max_iteration) z = z*z + c ; bitmapData.SetPixel(x, y, spec[iteration%255].Color); } } } bmp->Unmap(bitmapData); } //--------------------------------------------------------------------------- void __fastcall TForm1::Button1Click(TObject *Sender) { TBitmap *bmp=new TBitmap(Image1->Width, Image1->Height); mandelbrot_to_bitmap(bmp, 25); Image1->Bitmap->Assign(bmp); bmp->Free(); } |
Here we defined a very basic color spectrum ( spec[] ) and we try to keep drawing pixels simple. We are sure you will enjoy to survey drawing this better. Also you can find more fractal examples on VCL here. I think it is easy to convert to FMX version as in given example above.
Note that spec[], color spectrum array can be done outside of mandelbrot_to_bitmap() as a global or public in a class;
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TAlphaColorRec spec[256]; |
and this line
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for(auto i=0; i<256; i++){ spec[i].A=0xFF; spec[i].R=i; spec[i].G=0; spec[i].B=i; } |
which setups color spectrum array can be defined outside of mandelbrot_to_bitmap() to speed up this function. You can also directly draw to Image1->Bitmap without doing Assign() and Free(). Iterations and some other coding techniques may also speed up calculation and drawing durations. This simple code do all you need in one procedure.
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