After experimenting with my program for two days, I found that the use of `degree` within the methods `checkDegreeOfDivergence` and `createRandomColors` does not increase the quality of the pictures and so I removed it. 

Also to increase the variety of colors I changed the following code

    public static Color[] createRandomColors(int degree)
    {
        Color[] colors = new Color[degree+1];
        colors[degree] = new Color(0,0,0);
        double r = Math.random();
        int red = 0, green = 0, blue = 0;
        for (int i = 0; i < degree; i++)
        {
            red = 13*(256-i) % 256;
            green = 7*(256-i) % 256;
            blue = 11*(256-i) % 256;
            colors[i] = new Color(red,green,blue);
        }
        return colors;
    }

into

        public static Color[] createRandomColors()
            {
                Color[] colors = new Color[256];
                double r = Math.random();
                int red = 0, green = 0, blue = 0;
                if (r < 1.0/6.0) 
                {
                    for (int i = 0; i < 256; i++)
                    {
                        red = randomize(10,16)*(256-i) % 256;
                        green = randomize(4,10)*(256-i) % 256;
                        blue = randomize(8,14)*(256-i) % 256;
                        colors[i] = new Color(red,green,blue);
                    }
                }
                else if (r < 2.0/6.0) 
                {
                    for (int i = 0; i < 256; i++)
                    {
                        red = randomize(10,16)*(256-i) % 256;
                        green = randomize(4,10)*(256-i) % 256;
                        blue = randomize(8,14)*(256-i) % 256;
                        colors[i] = new Color(red,blue,green);
                    }
                }
                else if (r < 3.0/6.0) 
                {
                    for (int i = 0; i < 256; i++)
                    {
                        red = randomize(10,16)*(256-i) % 256;
                        green = randomize(4,10)*(256-i) % 256;
                        blue = randomize(8,14)*(256-i) % 256;
                        colors[i] = new Color(green,red,blue);
                    }
                }
                else if (r < 4.0/6.0) 
                {
                    for (int i = 0; i < 256; i++)
                    {
                        red = randomize(10,16)*(256-i) % 256;
                        green = randomize(4,10)*(256-i) % 256;
                        blue = randomize(8,14)*(256-i) % 256;
                        colors[i] = new Color(green,blue,red);
                    }
                }
                else if (r < 5.0/6.0) 
                {
                    for (int i = 0; i < 256; i++)
                    {
                        red = randomize(10,16)*(256-i) % 256;
                        green = randomize(4,10)*(256-i) % 256;
                        blue = randomize(8,14)*(256-i) % 256;
                        colors[i] = new Color(blue,red,green);
                    }
                }
                else if (r < 6.0/6.0) 
                {
                    for (int i = 0; i < 256; i++)
                    {
                        red = randomize(10,16)*(256-i) % 256;
                        green = randomize(4,10)*(256-i) % 256;
                        blue = randomize(8,14)*(256-i) % 256;
                        colors[i] = new Color(blue,green,red);
                    }
                }
                return colors;
            }

    
and so the whole program changes as follows

    
    import java.awt.Color;
    
    public class MandelbrotSet
    {
        public static int checkDegreeOfDivergence(Complex c)
        {
            Complex nextRecurrence = c;
            for (int i = 0; i < 255; i++)
            {
                if (nextRecurrence.abs() >= 2) return i;
                nextRecurrence = nextRecurrence.times(nextRecurrence).plus(c);
            }
            return 255;
        }
        public static int checkDegreeOfDivergenceForMandelblar(Complex c, int degree)
        {
            Complex nextRecurrence = c;
            for (int i = 0; i < 255; i++)
            {
                if (nextRecurrence.abs() >= 2) return i;
                nextRecurrence = (nextRecurrence.conjugate()).times(nextRecurrence.conjugate()).plus(c);
            }
            return 255;
        }
        public static int randomize(int left, int right)
        {
            return left + (int) Math.random()*(right-left);
        } 
        public static Color[] createRandomColors()
        {
            Color[] colors = new Color[256];
            double r = Math.random();
            int red = 0, green = 0, blue = 0;
            if (r < 1.0/6.0) 
            {
                for (int i = 0; i < 256; i++)
                {
                    red = randomize(10,16)*(256-i) % 256;
                    green = randomize(4,10)*(256-i) % 256;
                    blue = randomize(8,14)*(256-i) % 256;
                    colors[i] = new Color(red,green,blue);
                }
            }
            else if (r < 2.0/6.0) 
            {
                for (int i = 0; i < 256; i++)
                {
                    red = randomize(10,16)*(256-i) % 256;
                    green = randomize(4,10)*(256-i) % 256;
                    blue = randomize(8,14)*(256-i) % 256;
                    colors[i] = new Color(red,blue,green);
                }
            }
            else if (r < 3.0/6.0) 
            {
                for (int i = 0; i < 256; i++)
                {
                    red = randomize(10,16)*(256-i) % 256;
                    green = randomize(4,10)*(256-i) % 256;
                    blue = randomize(8,14)*(256-i) % 256;
                    colors[i] = new Color(green,red,blue);
                }
            }
            else if (r < 4.0/6.0) 
            {
                for (int i = 0; i < 256; i++)
                {
                    red = randomize(10,16)*(256-i) % 256;
                    green = randomize(4,10)*(256-i) % 256;
                    blue = randomize(8,14)*(256-i) % 256;
                    colors[i] = new Color(green,blue,red);
                }
            }
            else if (r < 5.0/6.0) 
            {
                for (int i = 0; i < 256; i++)
                {
                    red = randomize(10,16)*(256-i) % 256;
                    green = randomize(4,10)*(256-i) % 256;
                    blue = randomize(8,14)*(256-i) % 256;
                    colors[i] = new Color(blue,red,green);
                }
            }
            else if (r < 6.0/6.0) 
            {
                for (int i = 0; i < 256; i++)
                {
                    red = randomize(10,16)*(256-i) % 256;
                    green = randomize(4,10)*(256-i) % 256;
                    blue = randomize(8,14)*(256-i) % 256;
                    colors[i] = new Color(blue,green,red);
                }
            }
            return colors;
        }
        public static void main(String[] args)
        {
            int width = Integer.parseInt(args[0]);
            int height = Integer.parseInt(args[1]);
            double x = Double.parseDouble(args[2]);
            double y = Double.parseDouble(args[3]);
            double zoom = Double.parseDouble(args[4]);
            Picture mandelbrotSet = new Picture(width,height);
            Color[] colors = createRandomColors();
            for (int j = 0; j < width; j++)
            {
                for (int i = 0; i < height; i++)
                {
                    double realPart = x + zoom*j/width;
                    double imaginaryPart = y + zoom*i/height;
                    Complex c = new Complex(realPart,imaginaryPart);
                    int degreeOfDivergence = checkDegreeOfDivergence(c);
                    Color color = colors[degreeOfDivergence];
                    mandelbrotSet.set(j,i,color);       
                }
            }
            mandelbrotSet.show();
        }
    }