With this little renderer application (written in Java), you can observe how the Buddhabrot is rendered.
Download ZIP file containing the Buddhabrot JAR. Run the JAR (
java -jar buddhabrot-0.0.1-SNAPSHOT.jar
or double-click the JAR) and click anywhere in the main window.
Hit the Toggle Axis button to show the complex plane axes.
These are all renders obtained by slightly modifying the original Mandelbrot equation.