An aiming sight includes a controller, a power supply, an LED array, and a collimator. The power supply powers the LEDs to turn-on and turn-off, and powers the collimator to rotate. The collimator rotates to different rotational positions while the controller, the power supply, and the LED array remain fixed in place. The LEDs are positioned such that one LED and the collimator are at a constant angle and separated by a constant focal distance for each collimator position. The controller controls the collimator to rotate to a collimator position to generate an aiming dot at an angular position corresponding to the collimator position. The controller turns-on the LED which is at the constant angle and separated from the collimator by the constant focal distance and turns-off the remaining LEDs such that the collimator collimates light from the turned-on LED into the aiming dot at the angular position corresponding to the collimator position.