In the Amber series, several characters had the ability to draw a picture that then would be a trump, and enable communications and even teleportation. What is it in the drawing that gives it such power?
Richard's answer makes sense (that it draws on the power of the Pattern/Logrus) but there's probably more to it than that...when Corwin is imprisoned in the first book, he's stuck in the cell until Dworkin happens by to draw him an exit on the wall. If one could just draw on the pattern himself to create a trump/exit, why didn't Corwin just do it himself? For that matter, why would the trump decks be so prized and valuable, if just anyone could create them? I think the point is that they are something that very few people can do (Dworkin/Merlin).
When Merlin created a trump he called on The Logrus. We can assume – as it is never described in detail – that the Amberites can call on The Pattern in the same way.
If you read the Dawn of Amber there is a scene in which Oberon is speaking with Dworkin about creating Trumps. Oberon commented that Dworkin creates the card using a different technique than he'd seen his brother use. His brother always had The Logrus as the starting point in the background and painted the rest of the scene over it whereas Dworkin did not draw The Logrus at all.
Dworkin commented that Oberon's brother was just copying Dworkin's early experiments and that drawing The Logrus was not what gave the Trump its power, rather holding The Logrus in the mind of the painter is what imbued it with power. Painting The Logrus had no effect other than to help the painter keep focused on that which conferred power.
I myself wondered about this question. As we learn, the trumps themselves do not hold much power. It is the skill of the card holder that counts. What the cards do is merely help those who walked the Pattern / navigated the Logrus to focus their strength, to concentrate on the subject. Throughout the books there are several examples of communication and teleportation without the use of trumps that was achieved merely by deep concentration. Of course, Dworkin is one hell of a painter, and his paintings are very much lifelike, which must contribute considerably to the beneficial effect of the trumps he painted. As was stated above, the lighthouse painting wasn't intentionally painted as a trump by Dworkin, and yet it served Corwin well enough. Perhaps a weaker character wouldn't be able to leverage the sketch for a trump-like effect. In my opinion, anyone who can travel through shadow and paint considerably well, can produce trump like objects.