Space Filling Curves

Series: Topology Series

Duration: 26

Creator: Intl Film Bureau Inc

Format: 16mm

Color: Color

Sound: sound

Description: Illustrates the concept of a limit curve, as specified by a sequence of approximation curves and applies it to the construction of space filling curves in the production of a 16-millimeter film. , Replicates Peano's topological construction which states that a curve of infinite length and zero area covers a square provided that two conditions are satisfied: (1) every point on the curve approaches a limit point and (2) the limit points fit together to make a curve. Uses the method of successive approximations to trace the movement of a single point on the space filling curve and then an array of points as they move toward the limit curve. Uses computer animation and camera zoom to show point movement toward the limiting curve, which is the square.

Complete Record: Illustrates the concept of a limit curve, as specified by a sequence of approximation curves and applies it to the construction of space filling curves in the production of a 16-millimeter film. , Replicates Peano's topological construction which states that a curve of infinite length and zero area covers a square provided that two conditions are satisfied: (1) every point on the curve approaches a limit point and (2) the limit points fit together to make a curve. Uses the method of successive approximations to trace the movement of a single point on the space filling curve and then an array of points as they move toward the limit curve. Uses computer animation and camera zoom to show point movement toward the limiting curve, which is the square.NOTE: Two (or more) records have been merged together to create this data.