The primes in the Gaussian integers — numbers of the form a + bi — are a fascinating object of study. For example, 2 is not prime as it factors as (1 + i) (1 − i); 3 remains prime. One can ask how far one can walk in the Gaussian primes starting near the origin at 1 + i and taking steps of size no greater than k. The cover image shows how far one can get with steps up to size 3. One runs into an impassable moat at radius just less than 100. A famous conjecture asserts that there is always such a moat, regardless of how large k is.