Glossary of Terms

a set of numerical values toward which the result of an iterated function is drawn, or attracted
branching, or splitting, as in the branches of a tree, or a fork
bifurcation diagram
a diagram produced (by iteration) in which bifurcation is a pronounced characteristic
the computer program supplied with this text which produces a bifurcation diagram
a state or condition which has no apparent orderly or predictable progression
the value assumed by a variable or parameter when none has been supplied by the user (of a program)
Disk Operating System; a computer program, or set of programs, that manages the storage and retrieval of data on a disk drive, and performs other necessary computer functions
Euclidean geometry
a branch of mathematics dealing with the relationships between points, lines, polygons, etc. Named for Euclid, an ancient scholar who formulated many of the fundamental ideas still in use today
a portion of a function's output which is returned, or 'fed back' to its input
a set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension; a set (of numbers which may define an object or image) having a non-integer dimension
fractal geometry
a branch of mathematics dealing with the study of fractals
a entity which acts upon an input to produce an output; an equation
geometry of nature
see fractal geometry
the computer program supplied with this text which performs iteration of a function and displays or prints the results
a mathematical process involving the repetitive solution of a function using feedback
Mandelbrot, Benoit
a mathematician who founded the branch of mathematics known as fractal geometry
Malthus, Sir Thomas
an 18th-century economist whose theories on population growth can be expressed in a 'population equation', which can then be iterated to produce a bifurcation diagram. The actual statements of his theories are irrelevant to the study of fractals; the equations and their unusual behavior are modern-day discoveries
Malthusian Theory
a popular name for the theory of Sir Thomas Malthus
mathematical monster
a term used in the 19th century to describe some of the early mathematical experiments which are now studied in fractal geometry
a state or condition which is stable or predictable
a type of variable which places controls or conditions on a process; the user can usually modify the parameters to observe specific results
population equation
an equation used to represent the growth of populations, containing a feedback element which represents the the factors that influence such growth
seed value
an initial starting value for a variable in an iterated function
a phenomenon where a small portion of an image or object, when magnified, resembles the original
strange attractor
an attractor that does not appear to consist of a finite number of elements. The set of values in a strange attractor often fall within a range of values. Often associated with chaotic regions of fractal images
to magnify


  1. The Fractal Geometry of Nature/Benoit B. Mandelbrot; © 1983 W.H. Freeman and Co. ISBN 0-7167-1186-9
  2. Dynamical Systems and Fractals/Karl-Heinze Becker; © 1989 Cambridge University Press ISBN 0-521-36910-X
  3. Fractal Programming in Turbo Pascal/Roger T. Stevens; © 1990 M & T Publishing ISBN 1-55851-106-7
  4. Chaos and Fractals, The Mathematics Behind the Computer Graphics/Robert L. Devaney and Linda Keen, Ed. Proceedings of Symposia in Applied Mathematics, Vol. 39; © 1989 The American Mathematical Society ISBN 0-8218-0137-6