1. A computing device comprising: at least one processor; a display screen; and a memory device including instructions that, when executed by the at least one processor, cause the computing device to: display a first displayable element using a first set of pixels of the display screen during a first period of time; render, during at least a portion of the first period of time, a second displayable element that is to be displayed using at least a portion of the first pixels during a second period of time after the first period of time, the second displayable element corresponding to a first virtual depth value set by a virtual depth system of the computing device; store the second displayable element to a portion of the memory device; acquire a stored copy of the second displayable element from the portion of the memory device; reduce an image size of the stored copy to produce a downscaled copy; apply a blurring technique to the downscaled copy to produce a blurred copy, the blurring technique being applied to the downscaled copy in a first direction and in a second direction, the first direction being orthogonal to the second direction; enlarge the blurred copy to produce an up-scaled copy, the up-scaled copy being enlarged to the image size prior to being reduced; apply a transparency filter to the up-scaled copy to produce a transparent copy; apply a color filter to the transparent copy to generate a virtual shadow for the second displayable element; identify a third displayable element on which the virtual shadow is to be displayed during the second period of time, the third displayable element corresponding to a second virtual depth value below the first virtual depth value; determine an area on the third displayable element at which to display at least a portion of the virtual shadow; and display at least the portion of the virtual shadow at the area on the third displayable element during the second period of time.