Calculation of chemotactic jump probabilities pc for the 2D-lattice example of Fig. 2.

The chemotactic attraction vector C is oriented 30° from u(1). The cosines of the angles between C and the jump vectors for neighbour sites 4, 5, 6 and 7 are all negative, therefore probabilities of jumps in these directions are zero. Note that the probability of jump u(1) is slightly greater than that of jump u(2), even though C is closer to u(2) than to u(1). This is because jump u(2) has length √2 = 1.414, compared with 1.0 for u(1), therefore when weighted by the length, the expected jump in direction 2 exceeds that for direction 1.