Angles less than 45° produce a fractal that is less tightly "curled". If using an iterated function system (IFS, or the chaos game IFS-method actually), then the construction of the C curve is a bit easier. It will need a set of two "rules" which are: Two points in a plane (the translators), each associated with a scale factor of 1/. The first rule is a rotation of 45° and the second −45°. This set will iterate a point ["x", "y"] from randomly choosing any of the two rules and use the parameters associated with the rule to scale/rotate and translate the point using a 2D-transform function. Put into formulae:  from the initial set of points formula_3. // Java Sample Implementation of Levy C Curve  import java.awt.Color; import java.awt.Graphics; import java.awt.Graphics2D; import javax.swing.JFrame; import javax.swing.JPanel; import java.util.concurrent.ThreadLocalRandom;  public class C_curve extends JPanel {