https://github.com/sds100/mandelbrotset
A C# Windows Forms application to view the Mandelbrot Set.
https://github.com/sds100/mandelbrotset
csharp dotnet mandelbrot mandelbrot-fractal mandelbrot-sets mandelbrot-viewer windows-forms zoomable
Last synced: about 1 month ago
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A C# Windows Forms application to view the Mandelbrot Set.
- Host: GitHub
- URL: https://github.com/sds100/mandelbrotset
- Owner: sds100
- License: gpl-3.0
- Created: 2018-04-29T11:37:13.000Z (about 8 years ago)
- Default Branch: master
- Last Pushed: 2018-06-22T16:08:05.000Z (almost 8 years ago)
- Last Synced: 2025-02-26T02:42:41.747Z (over 1 year ago)
- Topics: csharp, dotnet, mandelbrot, mandelbrot-fractal, mandelbrot-sets, mandelbrot-viewer, windows-forms, zoomable
- Language: C#
- Homepage:
- Size: 132 KB
- Stars: 0
- Watchers: 2
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# MandelbrotSet
A C# Windows Forms application to view the Mandelbrot Set.
## Roadmap
- [ ] Add rulers to the bottom and left side.
- [ ] Export .png image of a user desired portion of the Mandelbrot Set with a custom resolution
## Understanding the code
This is mainly for me so if I ever come back to this project, I can understand what my crazy mind was thinking. You can also read it to learn (maybe) about complex numbers and the Mandelbrot Set.
> ### What is a complex number?
> A complex number is a number expressed in the form a + bi where *a* and *b* are real numbers and *i* is an "imaginary number". For example 7 + 3*i* where *i* could be 
> ### The algorithm
> 
> *Z* and *C* are complex numbers.
For example, where  (the first iteration of Z) and C are ...
 because...
Therefore...
 is then substituted back into the formula.
### How do you write the algorithm in code?
The type of variable we choose to store Z and C as massively affects how far we can zoom in before bands start appearing down the screen. This happens because the limits of floating point precision are met. By using BigDecimal (in C#), we can overcome this but it is MUCH slower.
*i* can be represented by it's coefficient.
```c#
while (z_real * z_real + z_im * z_im < 4 && iteration < MAX_ITERATIONS)
{
double z_real_tmp = (z_real * z_real) - (z_im * z_im) + c_real;
z_im = 2 * z_real * z_im + c_im;
z_real = z_real_tmp;
}
```
 (z_real) is calculated from 
and
 (z_im) is calculated from . because...
The formula in its most basic terms is...  which simplifies to...
The real terms  are grouped together to calculate .  is the same as .
The complex terms  are grouped together to calculate .  is the same as .
### Using a ComplexNumber class
```c#
// Convert the pixel coordinate to the equivalent coordinate on the given portion of the complex plane.
double c_real = ((pixelCoords.X - bitmapWidth / 2) * planeWidth / bitmapWidth)
+ planeCentre.X;
double c_im = ((pixelCoords.Y - bitmapHeight / 2) * planeHeight / bitmapWidth)
+ planeCentre.Y;
var z = new ComplexNumber(0,0);
var c = new ComplexNumber(c_real, c_im);
int iteration = 0;
while (z.Normal < 4 && iteration < MAX_ITERATIONS)
{
z = z * z + c;
iteration++;
}
```
### How do you multiply two complex numbers?
For example, If we multiply out these brackets and simplify where *i* = 
And since we know that *i* is an imaginary number which is is the square-root of a real number.
= 
= 
= 
Therefore...
= 
= 
There we go!
 = 