In illustrative implementations, shape is used to encode computer passwords or other information. The passwords may be easy for a human to remember—and yet have an extremely high number of permutations (e.g., in some cases, greater than 1030 permutations, or greater than 10261 permutations, or greater than 106264 permutations). This combination of a password being easy for a human to remember—yet having a large number of permutations—offers many practical benefits. Among other things, the huge number of permutations makes the password extremely resistant to guessing attacks. In addition, in some cases, the passwords that are created with the shapes are highly resistant to attacks by keystroke logging, mouse logging, touch-gesture logging, screen logging, shoulder surfing, phishing, and social engineering. Alternatively, the shapes may be used to encode other information, such as information that uniquely identifies a product or a machine part.