A friend of mine, an expert in statistical genomics, told me the following story: At a dinner party, an attractive lady asked him, “What do you do for a living?” He replied, “I model.” As my friend is a handsome man, the lady did not question his statement and continued, “What do you model?” “Genes.” She then looked at him up and down and said, “Mh, you must be very much in demand.” “Yes, very much so, especially after I helped discover a new culprit gene for a common childhood disease.” The lady looked puzzled.

Very simple mathematical equations can give rise to surprisingly complicated, chaotic dynamics, with behavior that is sensitive to small deviations in the initial conditions. We  illustrate this with a single recurrence  equation that can be  easily simulated, and with mixing in simple fluid flows.