8.13. DEMOS

colored

for each point on screen P:
iterations = if check_if_is_in_set (P)
map iterations to color
draw color point

The integer version is where the operations on complex numbers are replaced with integer operations
according to the rules which were explained above.

Listing 8.25: For integer numbers

def check_if_is_in_set(X, Y):
X_start=X
Y_start=Y
iterations=0

while True:

if (X^2 + Y^2 > bounds):

break

new_X=X^2 - Y^2 + X_start

new_Y=2*X*Y + Y_start

if iterations > max_iterations:

break

iterations++

return iterations

black-white

for X = min_X to max_X:
for Y = min_Y to max_Y:
if check_if_is_in_set (X,Y) < max_iterations:
draw point at X, Y

colored

for X = min_X to max_X:
for Y = min_Y to max_Y:
iterations = if check_if_is_in_set (X,Y)
map iterations to color
draw color point at X,Y

Here is also a C# source which is present in the Wikipedia article^51 , but we’ll modify it so it will print the
iteration numbers instead of some symbol^52 :

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Mnoj
{
class Program
{
static void Main(string[] args)
{
double realCoord, imagCoord;
double realTemp, imagTemp, realTemp2, arg;
int iterations;
for (imagCoord = 1.2; imagCoord >= -1.2; imagCoord -= 0.05)
{
for (realCoord = -0.6; realCoord <= 1.77; realCoord += 0.03)
{
iterations = 0;
realTemp = realCoord;
imagTemp = imagCoord;
arg = (realCoord realCoord) + (imagCoord imagCoord);
while ((arg < 2*2) && (iterations < 40))
{

(^51) wikipedia
(^52) Here is also the executable file:beginners.re