Minkowski to Penrose
Watch a Minkowski spacetime diagram squeeze into a Penrose diamond.
Minkowski spacetime diagram with hyperbolas of constant interval and a grid of constant time and position, morphing into a Penrose diamond as a slider moves or the play button runs.
Minkowski
light cone, the "X"
timelike hyperbolas
spacelike hyperbolas
constant t and x
Every stage of the slider is itself a valid squeeze, so light rays stay at 45° the whole way. The outline is where infinity sits at that stage: it starts far off the canvas and closes in until it is the Penrose diamond. The light-cone X shrinks so its ends become the midpoints of the diamond's edges. The hyperbolas curl inward and bunch up along the edges ℐ⁺ and ℐ⁻. Lines of constant t pinch to the side corners i⁰; lines of constant x pinch to the top and bottom corners i⁺ and i⁻.