Mandelbrot set in 50 lines of C++
Explanation
Lets include the libraries we’ll need to plot the mandelbrot set
#include <SDL2/SDL.h>
#include <numeric>
#include <complex>
Now we’re going to create a function to decide if some complex number c is in
the set. We’re going to define a function
int is_in_set(std::complex<double> c) this function will decide if the complex
number c is in the set and return to us 0 if it is. Otherwise it will return
some number depending on how many iterations it took to decide that it was not.
int is_in_set(std::complex<double> c)
{
// create a complex number z
//
std::complex<double> z(0,0);
// check if z ever exceeds our set limit of 10
// and return how many iterations it took to determin that
//
for(int i = 0; i < 2500; i++)
{
z = std::pow(z,2) + c;
if(std::norm(z) > 10)
{
return i;
}
}
// if z never exceeded our bounds return 0
//
return 0;
}
This function is all you need to decide if some point c is in the set or not.
We take a c initialize z to (0,0) then iterate 2500 times to see if the
squared magnitude of z ever exceeds 10 (an arbitrary number I made up, feel
free to change it to whatever you want).
Next we’re going to loop over x and y and run the is_in_set function for
every (x,y) to see if the (x,y) combination lands in the set.
int iters = 0;
for(double x = -2.0; x < 2.0; x+=0.001)
{
for(double y = -2.0; y < 2.0; y+=0.001)
{
iters = is_in_set(std::complex<double>(x,y);
// If iters == 0 paint this point black.
// Otherwise paint the point
// a color depending on the number of iters
}
}
doing this will give you something similar to this.
The full source code is available below:
#include <SDL2/SDL.h>
#include <numeric>
#include <complex>
int is_in_set(std::complex<double> c)
{
std::complex<double> z(0,0);
for(int i = 0; i < 2500; i++)
{
z = std::pow(z,2) + c;
if(std::norm(z) > 10)
{
return i;
}
}
return 0;
}
int main()
{
SDL_Init(SDL_INIT_EVERYTHING);
SDL_Window* window = nullptr;
SDL_Renderer* renderer = nullptr;
SDL_CreateWindowAndRenderer(
1000*2,
1000*2,
0,
&window,
&renderer);
SDL_RenderSetScale(renderer,2,2);
for(double x = 0.0; x < 1.0; x+=0.001)
for(double y = 0.0; y < 1.0; y+=0.001)
{
double point_x = std::lerp(-2.0, 2.0,x);
double point_y = std::lerp(-2.0, 2.0,y);
int iters = is_in_set(
std::complex<double>(
point_x,
point_y
)
);
if(iters == 0)
{
SDL_SetRenderDrawColor(renderer,0,0,0,255);
SDL_RenderDrawPointF(
renderer,
static_cast<float>(x * 1000.0),
static_cast<float>(y * 1000.0)
);
}
else{
SDL_SetRenderDrawColor(
renderer,
static_cast<Uint8>(3 * iters % 255),
static_cast<Uint8>(3 * iters % 255),
static_cast<Uint8>(3 * iters % 255),
255);
SDL_RenderDrawPointF(
renderer,
static_cast<float>(x * 1000.0),
static_cast<float>(y * 1000.0));
}
}
SDL_RenderPresent(renderer);
SDL_Delay(10000);
}