Abstract: Julia curves, and their relation to the Mandelbrot set, are explained.

REC/C is one of a series of specialized REC programs; in this case one which acts like a hand held graphing calculator for complex arithmetic.

Techniques used to plot contours in the package <PLOT> are described. Aside from its using traditional interpolation formulas, <PLOT> is characterized by taking pairs of triangles rather than rectangles for primitive domains, and for tracing out one entire contour before starting another, to minimize pen raising and lowering.

Detailed examination of the resonances in the Dirac harmonic oscillator, using results from the differential equation solver SERO.

As part of a collection of samples illustrating the use of the second order real differential equation solver SERO, some variants on the theme of periodic potentials are discussed. Constructing the stability chart for a periodic potential is one of the most important uses of the program, although details of specific solutions are also frequently called for.

REC-R is one of a series of specialized REC programs; in this case one which provides assistance in graphing the solutions of real, second order differential equations. It is therefore an adjunct to the program SERO which serves the same purpose.

In studying the symmetry groups of a crystal lattice in the presence of a magnetic field, the projective representations of these groups must be considered, because of the phase change in the wave functions which is due to the gauge transformations which accompany the geometric symmetries. These projective representations are ordinary representations of a group which is isomorphic to the generalized Dirac groups. The irreducible representations of the symmetry adapted functions of these groups can be obtained by means of techniques arising from the method of induced representations for those groups which can be exhibited as semi-direct products.

Para estudiar los grupos de simetría de una red cristalográfica en presencia de un campo magnético deben considerarse las representaciones proyectivas de dichos grupos, debido al cambio de fase que sufren las funciones de onda y que proviene de las transformaciones de norma que acompañan a las simetrías geométricas. Estas representaciones proyectivas son representaciones ordinarias de un grupo que es isomórfico a los grupos generalizados de Dirac. Las representaciones irreducibles y las funciones adaptadas a la simetría de dichos grupos se puede obtener mediante técnicas que resultan del método de representaciones inducidas para los grupos que se pueden exhibir como productos semi-directos.

REC-F is one of a series of specialized REC programs; in this case one which provides assistance in designing flexagons. Flexagons were popularized by Martin Gardner in Scientific American in the early 1960's. It is still possible to read his descriptions inasmuch as the original articles have since been reprinted in various collections of his articles. Basically, a flexagon is a fractal derived from a stack of polygons which can be folded back and forth, preferably coming to rest in a plane; so they resemble dragon curves and Lindenmayer L-systems. The purpose of REC-F is to draw the frieze of polygons which will eventually be folded up to make a given flexagon.