CSC1321 Programming Assignment

Problems

Write programs for the following problems

1. Write a C++ program to generate a web page showing color gradients. Feel free to use your favorite color for the pattern. Note that the pattern actually consists of stripes with different color tones.
   Sample output.
   Mono-color variation

                  
   	//Sample skeleton program             
   	using namespace std;
   								 
   	int main()
   	{
   	  int r, g, b;
   
   	  for(int i = 0; i < 256; i++)
   	  {
   		  r = 0;
   		  g = 0;
   		  b = i;
   	  }
   
   	  return 0;
   	}
   

2. Write a C++ program to generate a web page showing color gradients.
   Sample output.
   Two-color variation controled by a periodic sine function.

                  
   	//Sample skeleton program             
   	using namespace std;
   	#define PI           3.14159265358979323846
   
   	int main()
   	{
   	  int r, g, b;
   	  double phaseShift = PI/3;
   
   	  for(int i = 0; i < 360 * 3; i++)
   	  {
   	      
   		  r = 256/2 * sin(i * PI / 180 + phaseShift) + 256/2;
   		  g = 0;
   		  b = 256/2 * sin(i * PI / 180) + 256/2;
   	  }
   
   	  return 0;
   	}
   

3. Write a program to calculate the following expression with 100 nested levels: \( S = \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+ \dots}}}} \) Hint: Think about the relationships: \(S_1 = 0\), \(S_{2} = \sqrt{1 + S_1}\), \(S_{3} = \sqrt{1 + S_2}\), \(\dots\), \(S_{i+1} = \sqrt{1 + S_i}\) when there are many nested levels of square roots in the expression
4. Write a program to calculate the following expression with 100 nested levels: \( S = 1+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{\dots}}}} \)

What to submit

Submit both C++ program and HTML output file to Canvas by the midnight of the due day.