Fluid displacement in a continuum pressured by a variable constellation of source flows can be visualized as solutions of line integrals. The algorithms are based on complex potentials that provide exact solutions of the Navier-Stokes equation and allow users to specify both the location and flux strength of multiple sources. If relative strength and positioning of the sources are varied, a wide range of flow patterns and particle paths can be traced. Time-dependent variations in the strength of the sources can account for transient-flow problems. A further expansion is superposition of a background flow, which displaces the particle paths issued from the sources into concentrated plumes. The outlined modeling technique for visualization of multiple plume displacements is potentially relevant for a wide spectrum of practical situations. Detailed applications are possible, such as time tracking of groundwater-plume migration from a series of pollution sources, tracking of salt-feeder-stock flow and suture zone formation when salt issued from the stocks coalesces into a salt canopy, and designing of optimal spacing and relative pressure strength of multiple water injection wells in field-development plans for hydrocarbon production. Further applications are highlighted in the main text, including a simulation of geometrical features exposed in the Chao coulee (Chilean Andes).