Apparatus and methods for generating and tracing vortices include an actuator that is moved through a fluid is such a fashion as to produce a difference in pressure between two faces, so that the fluid is drawn from an area of higher pressure into an area of lower pressure around an edge of the actuator, thereby producing a vortex. A vortex generator produces vortices in air or other fluid, without an external chamber being required. The rotational velocity of such a vortex is greater than the rotational velocity of the actuator. The shape, size, and strength of the vortices can be controlled by varying one or more of the size, shape, and speed of the apparatus' actuator including its leading and trailing edges, height of the actuator above the surface, and the angles between the plane of the actuator and the motion through the fluid. A vortex may be visualized easily using a tracing material which is introduced into the vortex. Vortices so produced can be used as amusements or for research into the ways in which vortices interact with structures, including airfoils, vehicles, buildings or other structures.