Task: Archimedean spiral
C++: #include <windows.h>
#include <string>
#include <iostream>
 
const int BMP_SIZE = 600;
 
class myBitmap {
public:
    myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {}
    ~myBitmap() {
        DeleteObject( pen ); DeleteObject( brush );
        DeleteDC( hdc ); DeleteObject( bmp );
    }
    bool create( int w, int h ) {
        BITMAPINFO bi;
        ZeroMemory( &bi, sizeof( bi ) );
        bi.bmiHeader.biSize        = sizeof( bi.bmiHeader );
        bi.bmiHeader.biBitCount    = sizeof( DWORD ) * 8;
        bi.bmiHeader.biCompression = BI_RGB;
        bi.bmiHeader.biPlanes      = 1;
        bi.bmiHeader.biWidth       =  w;
        bi.bmiHeader.biHeight      = -h;
        HDC dc = GetDC( GetConsoleWindow() );
        bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );
        if( !bmp ) return false;
        hdc = CreateCompatibleDC( dc );
        SelectObject( hdc, bmp );
        ReleaseDC( GetConsoleWindow(), dc );
        width = w; height = h;
        return true;
    }
    void clear( BYTE clr = 0 ) {
        memset( pBits, clr, width * height * sizeof( DWORD ) );
    }
    void setBrushColor( DWORD bClr ) {
        if( brush ) DeleteObject( brush );
        brush = CreateSolidBrush( bClr );
        SelectObject( hdc, brush );
    }
    void setPenColor( DWORD c ) {
        clr = c; createPen();
    }
    void setPenWidth( int w ) {
        wid = w; createPen();
    }
    void saveBitmap( std::string path ) {
        BITMAPFILEHEADER fileheader;
        BITMAPINFO       infoheader;
        BITMAP           bitmap;
        DWORD            wb;
        GetObject( bmp, sizeof( bitmap ), &bitmap );
        DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];
        ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) );
        ZeroMemory( &infoheader, sizeof( BITMAPINFO ) );
        ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );
        infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
        infoheader.bmiHeader.biCompression = BI_RGB;
        infoheader.bmiHeader.biPlanes = 1;
        infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader );
        infoheader.bmiHeader.biHeight = bitmap.bmHeight;
        infoheader.bmiHeader.biWidth = bitmap.bmWidth;
        infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );
        fileheader.bfType    = 0x4D42;
        fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER );
        fileheader.bfSize    = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;
        GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );
        HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, 
                                  FILE_ATTRIBUTE_NORMAL, NULL );
        WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL );
        WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL );
        WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL );
        CloseHandle( file );
        delete [] dwpBits;
    }
    HDC getDC() const     { return hdc; }
    int getWidth() const  { return width; }
    int getHeight() const { return height; }
private:
    void createPen() {
        if( pen ) DeleteObject( pen );
        pen = CreatePen( PS_SOLID, wid, clr );
        SelectObject( hdc, pen );
    }
    HBITMAP bmp; HDC    hdc;
    HPEN    pen; HBRUSH brush;
    void    *pBits; int    width, height, wid;
    DWORD    clr;
};
class spiral {
public:
    spiral() {
        bmp.create( BMP_SIZE, BMP_SIZE );
    }
    void draw( int c, int s ) {
        double a = .2, b = .3, r, x, y;
        int w = BMP_SIZE >> 1;
        HDC dc = bmp.getDC();
        for( double d = 0; d < c * 6.28318530718; d += .002 ) {
            r = a + b * d; x = r * cos( d ); y = r * sin( d );
            SetPixel( dc, ( int )( s * x + w ), ( int )( s * y + w ), 255 );
        }
        
        bmp.saveBitmap( "./spiral.bmp" );
    }
private:
    myBitmap bmp;
};
int main(int argc, char* argv[]) {
    spiral s; s.draw( 16, 8 ); return 0;
}

Java: import java.awt.*;
import static java.lang.Math.*;
import javax.swing.*;

public class ArchimedeanSpiral extends JPanel {

    public ArchimedeanSpiral() {
        setPreferredSize(new Dimension(640, 640));
        setBackground(Color.white);
    }

    void drawGrid(Graphics2D g) {
        g.setColor(new Color(0xEEEEEE));
        g.setStroke(new BasicStroke(2));

        double angle = toRadians(45);

        int w = getWidth();
        int center = w / 2;
        int margin = 10;
        int numRings = 8;

        int spacing = (w - 2 * margin) / (numRings * 2);

        for (int i = 0; i < numRings; i++) {
            int pos = margin + i * spacing;
            int size = w - (2 * margin + i * 2 * spacing);
            g.drawOval(pos, pos, size, size);

            double ia = i * angle;
            int x2 = center + (int) (cos(ia) * (w - 2 * margin) / 2);
            int y2 = center - (int) (sin(ia) * (w - 2 * margin) / 2);

            g.drawLine(center, center, x2, y2);
        }
    }

    void drawSpiral(Graphics2D g) {
        g.setStroke(new BasicStroke(2));
        g.setColor(Color.orange);

        double degrees = toRadians(0.1);
        double center = getWidth() / 2;
        double end = 360 * 2 * 10 * degrees;
        double a = 0;
        double b = 20;
        double c = 1;

        for (double theta = 0; theta < end; theta += degrees) {
            double r = a + b * pow(theta, 1 / c);
            double x = r * cos(theta);
            double y = r * sin(theta);
            plot(g, (int) (center + x), (int) (center - y));
        }
    }

    void plot(Graphics2D g, int x, int y) {
        g.drawOval(x, y, 1, 1);
    }

    @Override
    public void paintComponent(Graphics gg) {
        super.paintComponent(gg);
        Graphics2D g = (Graphics2D) gg;
        g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                RenderingHints.VALUE_ANTIALIAS_ON);

        drawGrid(g);
        drawSpiral(g);
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(() -> {
            JFrame f = new JFrame();
            f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
            f.setTitle("Archimedean Spiral");
            f.setResizable(false);
            f.add(new ArchimedeanSpiral(), BorderLayout.CENTER);
            f.pack();
            f.setLocationRelativeTo(null);
            f.setVisible(true);
        });
    }
}