How the two knobs work

Balance changes the relative probability of the two outcomes, from all 0 to all 1. Phase rotates the clock hand for the |1⟩ amplitude, showing its phase relative to the |0⟩ amplitude. The |0⟩ hand is the fixed reference. At the poles, the relative phase is physically irrelevant.

Filled area, not radius, represents the probability. Together the two controls can express every pure single-qubit state, but not arbitrary mixed states.

Try H → Z → H → MEASURE from |0⟩: the answer is always 1. Or turn BALANCE to 90° and see that the outcomes have equal probability.

Interactive concept for a potential physical busy board. In a real toy, the sliders would become robust rotary encoders and the circles could be displays behind protected windows. This is a classical simulator, not quantum hardware.