Even though 1.1 and 0.9 are very close together, the replacement rule sends iterates of 1.1 towards infinity and sends iterates of 0.9 towards zero. If you take the square root of 25, you will get 5. We saw in the last section that there is no way to square a real number and get a negative number as a result. Therefore, there is no real answer to the square root of -25. Julia sets are created using complex numbers.
Complex numbers have a real part and an imaginary part added together.
We can plot these complex numbers on a graph by letting the horizontal direction show the real part and the vertical direction show the imaginary part. We usually call the complex number at the end c for short. The computer begins with the point in the upper left corner of the screen. On the next iteration it takes the new z , squares it, and adds c. The computer assigns a color to the point based on how many iterations it takes for the number to escape.