We don't need no propagation
This little plant Cymbalaria muralis is known to me as ivy-leaved toadflax, a curiously unhelpful name since it refers to what it is not i.e. it is not toadflax although its flowers are similar in snapdragon shape, and its leaves only resemble ivy to which again it is no relation.
However it has a myriad of alternative names, many referring to its clinging/trailing growth: Ivywort. Aaron's Beard. Climbing Sailor. Creeping Jenny. Mother of Millions. Mother of Thousands. Kenilworth ivy, Thousand Flower. Oxford-weed. Pedlar's Basket. Pennywort. Rabbits. Roving Jenny. Wandering Jew....
Its generic name refers to the cymbal-shaped pair of yellow bulges at the throat of the tiny flower and its specific name to its propensity to grow on walls. A prolific plant, it has followed stone-built structures all over the world.. It's not native to Britain and by some accounts, maybe fanciful, it first arrived in this country as a stowaway along with some Greek statuary dispatched from the Mediterranean. Its French name ruine de Rome suggests that its habit of sending its long roots deep into the interstices of old masonry has not always met with approval.
How it achieves its clingy connection with architecture is what makes this plant most remarkable. The flower are initially attracted to the light (phototropism) and push themselves outwards to advertise their wares to the bees that act as their pollinators. Once fertilized however the flowers straightway shun the light and turn their faces to the wall, thus burrowing their seeds right into the dark crevices where they will germinate and take root.
"None of that risky aerial or animal dispersal for us thank you, we keep our offspring close to home. And look how successful we have been."