Flow is one of the most powerful features of Phaser that allows one to follow the iterates of thousands of initial conditions starting in a rectangular box. To compute Flow, one needs to change the mouse function to selecting such a rectangular FlowBox and set the desired number of initial conditions in the FlowBox.

  1. FLOW: Mouse can be configured for various functions in Phaser. To use the mouse for selecting a FlowBox, click on the mouse selector widget (labeled IC by default) in the center of the ToolBar of Main application window and select FLOW.

  2. Number of ...: From the drop-down widget on the right, select the number of desired points in a FlowBox. The specified number (5000) of randomly chosen initial conditions lying in a FlowBox will be used.

  3. FlowBox: To select a FloxBox, press the left mouse button at the upper left corner of the desired box and while holding down the button move the mouse to the lower right corner of the box (the small rectangle in the figure above). As soon as you release the mouse button the specified number of solutions starting in the selected box will be computed. The color of the initial conditions is determined by the color of the first initial condition in the Initial Conditions panel of the Numerics Editor.

  By modifying other controls, one can customize FLOW. For example, by setting Start Plotting = 0 and Stop Plotting = 1, one can follow the action of a MAP (Anosov MAP) on a rectagular region as seen the figure above. In the figure below, about one dozen iterates of the initial rectangle are computed.