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Montecarlo method and JFrame (math and java problem)

I made a little program to approximate Pi and I would like to represent it. I started but I thought it would look better if the points outside the circle were red and the ones inside were green. I can't do it and I don't understand why the problem is there. I don't know if it is in pure math or in dev.
for(int i = 0; i<1000; i++) {
double x = Math.random() * (500-250) + 250;
double y = Math.random() * 250;
double applyformula = (x - 250)*(x - 250) + (y - 250) * (y - 250);
if(applyformula == y || (y*y) - 500 * y < applyformula ) {
g.fillOval((int) x,(int) y, 5, 5);
g.setColor(Color.GREEN);
} else {
g.fillOval((int) x,(int) y, 5, 5);
g.setColor(Color.RED);
}
}
If someone could help me, that will be perfect.

It could be done in a simpler way.
for (int i = 0; i < 1000; i++) {
double x = Math.random();
double y = Math.random();
double applyformula = (x * x) + (y * y);
if (applyformula <= 1) {
g.setColor(Color.GREEN);
} else {
g.setColor(Color.RED);
}
// Set the actual coordinates in a 250 pixels wide square.
x *= 250;
y *= 250;
g.fillOval((int) x, (int) y, 5, 5);
}

Want to generate random set of coordinates (Java/Swing)

I have a program in Java like this one (https://www3.ntu.edu.sg/home/ehchua/programming/java/J8a_GameIntro-BouncingBalls.html). It is the object oriented one after Example 2 but with some slightly changes.
I want to generate random coordinates for the balls to spawn. But they are not allowed to intersect each other at spawning moment. The generated coordinates are the top left corner of an rectangle around the circle.
So the coordinates need a minimum distance of 2 * ballRadius.
I only got ether coordinates that have the distance of 2 * ballRadius but then there are only unique coordinates for x and y. So i only got one ball per available y coordinate.
Example There could be a Ball at the red circle but the one left to it "blocks" the y coordinate.
Every other coordinates i get are intersecting each other.
Thats my code so far.
int uniqueXY[][] = new int[ballCount][2];
for (int i = 0; i < ballCount; i++) {
int tempx = 0;
int tempy = 0;
Boolean foundX = true;
Boolean foundY = true;
while(foundX && foundY) {
tempx = (int) (Math.random() * field.maxX); // generate random number in range of filed
tempy = (int) (Math.random() * field.maxY);
for (int j = 0; j < ballCount; j++) { // Here it should check if the number is within the given rules
if ((uniqueXY[j][0] - (2 * ballRadius) > tempx) || (uniqueXY[j][0] + (2 * ballRadius) < tempx)) {
foundX = false;
} else {
foundX = true;
if ((uniqueXY[j][1] - (2 * ballRadius) > tempy) || (uniqueXY[j][1] + (2 * ballRadius) < tempy)) {
foundY = false;
foundX = false;
break;
} else {
foundY = true;
break;
}
}
}
}
uniqueXY[i][0] = tempx;
uniqueXY[i][1] = tempy;

So I have come up with some new Code with the similar problem.
It calculates the distance between every set coordinate and the temporay ones. For the most part it works fine, it just behaves akward if I strees the code and force large numbers of balls.Example with 400 balls Only the balls at the border get forced together.
int uniqueXY[][] = new int[ballCount][2];
for (int k = 0; k < ballCount; k++) {
Boolean found = true;
while(found) {
int tempX = (int) (Math.random() * field.maxX); //create rnd x/y in range of field
int tempY = (int) (Math.random() * field.maxY);
if (k == 0) { // first case gets set, because nothing to compare
uniqueXY[k][0] = tempX;
uniqueXY[k][1] = tempY;
found = false;
break;
}
for (int j = 0; j < k; j++) { //calculates distance between every set coordinate and the temp
int erg1 = (int) (Math.pow(uniqueXY[j][0] - tempX, 2));
int erg2 = (int) (Math.pow(uniqueXY[j][1] - tempY, 2));
int distance = (int) Math.sqrt(erg1 + erg2);
if (distance < 60) { // if distance between coordinates < 60 temp gets discarded
found = true;
break;
}
if (j == k - 1) { // if every set case is checked and distance was always fine, temp gets set
uniqueXY[k][0] = tempX;
uniqueXY[k][1] = tempY;
found = false;
}
}
}
}

Java: Comparing two Bufferedimages using loops

When i want to check if two Bufferedimages are the same, i can simply compare them pixel by pixel using these two loops:
boolean bufferedImagesEqual(BufferedImage img1, BufferedImage img2) {
if (img1.getWidth() == img2.getWidth() && img1.getHeight() == img2.getHeight()) {
for (int x = 0; x < img1.getWidth(); x++) {
for (int y = 0; y < img1.getHeight(); y++) {
if (img1.getRGB(x, y) != img2.getRGB(x, y))
return false;
}
}
} else {
return false;
}
return true;
}
I took this from : Here
But I also want this to work if img2 is rotated by 90 or 270 degrees. I tried swtiching x and y , using combinations like
img2.getWidth()-x
in the second .getRGB() but none of it seems to work.
I know it may not be the hardest problem in the world but i cannot seem to figure it out.
Any help would be greatly appreciated.

I think it is unavoidable to perform the "2-loops" 3 times:
one for 0 degree rotation, the second 90 and the third 270:
For 90 degrees: (assert img1.getWidth()==img2.getHeight() && img1.getHeight()==img2.getWidth())
for (int x = 0; x < img1.getWidth(); x++) {
for (int y = 0; y < img1.getHeight(); y++) {
if (img1.getRGB(x, y) != img2.getRGB(img1.getHeight() - 1 - y, x))
return false;
}
}
For 270 degrees: (assert img1.getWidth()==img2.getHeight() && img1.getHeight()==img2.getWidth())
for (int x = 0; x < img1.getWidth(); x++) {
for (int y = 0; y < img1.getHeight(); y++) {
if (img1.getRGB(x, y) != img2.getRGB(y, img1.getWidth() - 1 - x))
return false;
}
}

For loops creating black screen without reading integer array

Whenever I tried to get the pixel array in the ori class, which extends the Screen class, to render to the canvas (that, in turn, is written in the canvas in the main class) it just generated a black image over the canvas in the JFrame. This only happened when the 'for' loops are written as "x = 0" as opposed to "int x = 0". When the loops are written as "int x = 0" or "int y= 0", it did not generate anything, including the black screen.
This is from the origin method in the ori class:
if(x <= ax && y <= ay){
for(int y = 0; y < height; y++){
for(int x = 0; x < width; x++){
pixels[x + y * width] = 0xff00ff;
}
}
}
screen class:
void waves(){
rand = new Random();
for(y = 0; y < height; y++){
int r = 24 + 1;
int s = 10;
waves++;
if(waves == 75){
sel = rand.nextInt(2);
waves = 0;
}
if(sel == 0){
if(blue > 0){
float f = ray - r;
double uir = f * 0.0001;
u = blue *= uir;
}
else{
}
}
if(sel == 1){
if(blue > 0){
float f = ray + r;
double uir = f * 0.0001;
u = blue *= uir;
}
else{
}
}
for(x = 0; x < width; x++){
Color wacol = new Color(0, 0, u);
int water = wacol.getRGB();
pixels[x + y * width] = water;
orga.origin();
}
}
}
It appears that the 'for' loops written as "x = 0" are called upon and then, somehow, render without reading the pixel array. The same happens when "int x = 0" but with the opposite result. What is causing this and what is causing the code to ignore the pixel array?

Processing/Line Graphing - Help

I posted something similar yesterday, but got nothing. I spent a few hours today problem-solving, but didn't progress any.
I'm using Processing (the language) and trying to implement a method that draws a line between two points. (I don't want to use the library's line() method.)
My lineCreate method works great for positive slopes, but fails with negative slopes. Can you help figure out why?
Here's the lineCreate() code:
void createLine(int x0, int y0, int x1, int y1){
//...
// Handle slanted lines...
double tempDX = x1 - x0;
double tempDY = y1 - y0; // Had to create dx and dy as doubles because typecasting dy/dx to a double data type wasn't working.
double m = (-tempDY / tempDX); // m = line slope. (Note - The dy value is negative
int deltaN = (2 * -dx); // deltaX is the amount to increment d after choosing the next pixel on the line.
int deltaNE = (2 * (-dy - dx)); // ...where X is the direction moved for that next pixel.
int deltaE = (2 * -dy); // deltaX variables are used below to plot line.
int deltaSE = (2 * (dy + dx));
int deltaS = (2 * dx);
int x = x0;
int y = y0;
int d = 0; // d = Amount d-value changes from pixel to pixel. Depends on slope.
int region = 0; // region = Variable to store slope region. Different regions require different formulas.
if(m > 1){ // if-statement: Initializes d, depending on the slope of the line.
d = -dy - (2 * dx); // If slope is 1-Infiniti. -> Use NE/N initialization for d.
region = 1;
}
else if(m == 1)
region = 2;
else if(m > 0 && m < 1){
d = (2 * -dy) - dx; // If slope is 0-1 -> Use NE/E initialization for d.
region = 3;
}
else if(m < 0 && m > -1){
d = (2 * dy) + dx; // If slope is 0-(-1) -> Use E/SE initliazation for d.
region = 4;
}
else if(m == -1)
region = 5;
else if(m < -1){
d = dy + (2 * dx); // If slope is (-1)-(-Infiniti) -> Use SE/S initialization for d.
region = 6;
}
while(x < x1){ // Until points are connected...
if(region == 1){ // If in region one...
if(d <= 0){ // and d<=0...
d += deltaNE; // Add deltaNE to d, and increment x and y.
x = x + 1;
y = y - 1;
}
else{
d += deltaN; // If d > 0 -> Add deltaN, and increment y.
y = y - 1;
}
}
else if(region == 2){
x = x + 1;
y = y - 1;
}
else if(region == 3){ // If region two...
if(d <= 0){
d += deltaE;
x = x + 1;
}
else{
d += deltaNE;
x = x + 1;
y = y - 1;
}
}
else if(region == 4){ // If region three...
if(d <= 0){
d += deltaSE;
x = x + 1;
y = y + 1;
}
else{
d += deltaE;
x = x + 1;
}
}
else if(region == 5){
x = x + 1;
y = y + 1;
}
else if(region == 6){ // If region four...
if(d <= 0){
d += deltaSE;
x = x + 1;
y = y + 1;
}
else{
d += deltaS;
y = y + 1;
}
}
point(x, y); // Paints new pixel on line going towards (x1,y1).
}
return;
}

Have a look at this page. It explains the whole theory behind line drawing with code examples.
There are a number of known algorithm for line drawing. Read about them here.