Creating Butterfly themed Fractal in C++ Using Graphics

Last Updated : 16 Dec, 2019

In Layman’s terms, Fractals are beautiful patterns brought into existence upon the intertwining of computation and mathematics. To get a bit technical they are recursive in nature such that when looked upon a certain subset of a given fractal a similar pattern appears to emerge out of it.

In this article, a new type of fractal pattern is generated, given as below:

Approach:

Recursively go to the end branch of a Fractal tree.
When the length of the branch reaches our threshold value, draw out that particular branch and exit out of the function.
To keep the colors similar for a few iterations, we use type casting since ((colorVal%15000)/1000+1) would give out spectrums of same values, i.e. same colour thousand times before it iterates.

Below is the implementation of the above approach:

// C++ code to Create a Butterfly  
// themed Fractal using Graphics 
  
#include <math.h> 
#include <stdlib.h> 
#include <winbgim.h> 
  
#define Y 1080 
#define X 1920 
  
// c is defined as the angle between each 
// iterative lines, changing this would result 
// in different and interesting patterns. 
#define c 5 * M_PI / 7 
  
// colorVal is used to provide different colors 
// for each iterating point/line in the cycle. 
int colorVal = 0; 
  
// The core function in the program which is 
// recursive in nature and terminates when the 
// line size is less than 0.1 pixels. 
int Pyt_Tree(float x, float y, float r, float ang) 
{ 
  
    // Max iteration condition so as to increase 
    // the accuracy of the fractal pattern. 
    // The closer it is to zero the higher the 
    // details but would cost more processing time. 
    if (r < 0.1) { 
  
        // combination of type casting and iteration 
        // so as to provide a Greatest Integer Function 
        // sort of manipulation for the color input. 
        setcolor((colorVal++ % 15000) / 1000 + 1); 
  
        // Conversion of the parametric coordinates 
        // of the points to the Argand coordinates 
        // while displaying them. 
        line(x, y, x - r * sin(ang), y - r * cos(ang)); 
  
        return 0; 
    } 
  
    float r_n; 
  
    if (c > M_PI / 4) { 
        r_n = sin(c); 
    } 
    else { 
        r_n = cos(c); 
    } 
  
    // Recursive calling of the Pyt_Tree() function 
    // to get towards the end of the branch of the 
    // fractal tree. 
    Pyt_Tree(x - r * sin(ang), y - r * cos(ang), 
             r / (2 * r_n), (ang + c)); 
    Pyt_Tree(x - r * sin(ang), y - r * cos(ang), 
             r / (2 * r_n), (ang - c)); 
  
    return 0; 
} 
  
// Driver code 
int main() 
{ 
    initwindow(X, Y); 
    Pyt_Tree(X / 2, Y, Y * 0.9, 0); 
    getch(); 
    closegraph(); 
    return 0; 
} 

Output:

Program to creating Doraemon cartoon character using Computer Graphics

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