whatConway's two rules: a live cell with two or three live neighbours survives; a dead cell with exactly three is born; everything else dies. A random soup boils, collides, collapses, and within a thousand generations burns down to ash: still lifes the rules cannot touch and oscillators ticking with period two, forever. The census counts them live, from the field itself.
whyThe claim: persistent MACHINES from two sentences of physics. Stability was nowhere in the rules and is everywhere in the outcome; and then a click stamps the Gosper glider gun, a thirty-six-cell machine discovered in 1970 that manufactures a spaceship every thirty generations and fires the stream across the ruins. Where the stream meets the debris it burns and builds; the census counts the gliders in flight by recognizing their shapes in every phase and orientation.
howA wrapped grid the size of your screen, twelve generations a second. Stills are cells unchanged for two generations, oscillators cells returning with period two, gliders matched exactly against isolated five-by-five masks. One integer seeds the soup, so the same seed burns down to the same ash.