The above applet shows the Laplace equation is action. This equation takes the voltage in a grid square and makes it a new value by averaging the surrounding values. If a square has a value of 100 then after one calculation the the new value would be zero. However the four surrounding squares would take on values of 25. The above demonstration is color coded to show the dispersion of voltage from the drawn parallel plate capacitor.
Use the on/off button to toggle the animation. Use the step button if only one calculation is required. The reset button will start you over again if pressed.
Key:
Black: -100 V
Dark Gray: The volts are between -99.9 and -80
Gray: The volts are between -79.9 and -60
Light Gray: The volts are between -59,9 and -40
Magenta: The volts are between -39.9 and -20
Blue: The volts are between -19 and -0.01
White: The volts are equal to zero
Green: The volts are between 0.01 and 19.9
Cyan: The volts are between 20 and 39.9
Yellow: The volts are between 40 and 59.9
Orange: The volts are between 60 and 79.9
Pink: The volts are between 80 and 99.9
Red: The volts are equal to 100