We present drozBot: le robot portraitiste, a robotic system that draws artistic portraits of people. The input images for the portrait are taken interactively by the robot itself. We formulate the problem of drawing portraits as a problem of coverage which is then solved by an ergodic control algorithm to compute the strokes. The ergodic computation of the strokes for the portrait gives an artistic look to them. The specific ergodic control algorithm that we chose is inspired by the heat equation. We employed a 7-axis Franka Emika robot for the physical drawings and used an optimal control strategy to generate joint angle commands. We explain the influence of the different hyperparameters and show the importance of the image processing steps. The attractiveness of the results was evaluated by conducting a survey where we asked the participants to rank the portraits produced by different algorithms.