A. G. Davis Philip

A new scaling along the spike of the Mandelbrot set

Abstract Using the zeros of a family of real polynomials, we locate a sequence of midgets along the spike of the Mandelbrot set. By this method we can readily find midgets (tiny copies of the Mandelbrot set) of high cycle number; we include a picture of a 200-cycle midget magnified by a factor of 5.68 × 10 238 . The ratios of distances between the cardioid centers for successive midgets in this sequence exhibit an asymptotic scaling, as does the ratio of head-to-center distances. We present evidence supporting a pattern of scalings for some “generalized Mandelbrot sets.”

Warped midgets in the Mandelbrot set

Abstract Warped midgets in the Mandelbrot set have been measured, using an algorithm that allows the positions of the head, and cardioid atoms (north and south) of any midget to be found, once one has placed the cursor on the computer terminal somewhere inside any midget. We describe two distortions of midgets: linear distortions and angular distortions. When the north and south angles are plotted in the north/south angle plane, families of points are formed. The angle and distance measures of warped midgets from the Sea Horse Valley of the Mandelbrot set and from other sea horse valleys of midgets, whether on the Spike or on tendrils above atoms, all fall closely together in one part of the north/south plane. Measures of warped midgets from tendrils above the major atoms on the surface of the Cardioid fall closely together in another part of the north/south plane. This different way of looking at the Mandelbrot set offers an interesting way of studying the distortions of midgets.

UBV color-magnitude diagrams of galactic clusters

Abstract A catalogue of over 37,000 UBV observations is now available in the form of 165 color-magnitude and color-color plots of galactic globular clusters. A bibliography of references is given and a table of data for 115 clusters summarizing much of the current information concerning globular clusters. The UBV observations are available on tape from the Strasbourg Stellar Data Center.

Multicolor CCD photometry of the open cluster NGC 752

The results of CCD photometry in the seven-color Vilnius system of 3058 stars down to V ∼ 18.0 mag in a 1.5 square degree field around the cluster NGC752 are presented. For most of the stars brighter than V =17.0 mag, photometric spectral and luminosity classes are determined. The catalog of 1174 stars down to V = 15.5 mag is given in the paper. The entire catalog will be available at the CDS Simbad database. The color-magnitude diagram indicates an extension of the cluster’s main sequence down to 5 mag below the turnoff point.

Chapter 51 – Warped midgets in the Mandelbrot set

Publisher Summary Warped midgets in the Mandelbrot set have been measured, using an algorithm that allows the positions of the head, and cardioid atoms (north and south) of any midget to be found, once the cursor has been placed on the computer terminal somewhere inside any midget. This chapter describes two distortions of midgets: linear distortions and angular distortions. When the north and south angles are plotted in the north/south angle plane, families of points are formed. The angle and distance measures of warped midgets from the Sea Horse Valley of the Mandelbrot set and from other sea horse valleys of midgets––whether on the Spike or on tendrils above atoms––all fall closely together in one part of the north/south plane.. This different way of looking at the Mandelbrot set offers an interesting way of studying the distortions of midgets.

Chapter 40 – A new scaling along the spike of the Mandelbrot set

Publisher Summary Using the zeros of a family of real polynomials, a sequence of midgets along the spike of the Mandelbrot set can be located. By this method, midgets (tiny copies of the Mandelbrot set) of a high cycle number can readily be found. The ratios of distances between the cardioid centers for successive midgets in this sequence exhibit an asymptotic scaling, as does the ratio of head-to-center distances. This chapter presents evidence supporting a pattern of scalings for some “generalized Mandelbrot sets.” The Mandelbrot set, M, is the collection of complex numbers c for which the Julia set Jc of Fc (z) = z2+c is connected. There are many sequences of midgets related through scalings of size. This chapter reviews some of the known sequences and reports on a new scaling of midgets, discovered along the real axis, progressing toward c = - 2 .

Precision CCD Photometry of the Horizontal Branch

The Stromgren four-color system is well suited to the measure and analysis of horizontal-branch stars. The increased accuracy of the CCD photometric system and the ability to measure fainter stars in very crowded regions make the combination of the CCD system and four-color photometry an excellent one to study horizontal-branch stars in globular clusters.

Elemental Abundances of Sharp-Lined Pop I Main Sequence B, A, and F Stars and Pop II A Stars

The elemental abundances of late B and early A stars should be among the most reliably derived as these stars have well known atmospheric physics, and non-crowded optical spectra with lines of many species with good oscillator strengths. We obtained elemental abundances of sharp-lined stars from high dispersion, S/N > 50, spectra taken at DAO and KPNO. We performed fine analyses using ATLAS6 and more recently ATLAS9 model atmospheres. Our papers (mostly in MNRAS) contain consistent studies of about 35 B3 to F7 superficially normal, Mercury-Manganese (HgMn), Am, and Field Horizontal Branch (FHB) A stars. The abundances of the normal main sequence B, A, and F stars are indicators of Galactic metallicity during the most recent epoch of Galactic history.

Four-Color Measures of BHB Stars in M 4, M 13 and M 55

Stromgren four-color photometric measures have been made of blue horizontal-branch A stars in the globular clusters M 4, M 13 and M 55 with the Steward Observatory 90 inch telescope and with the 60 inch telescope at Cerro Tololo Inter-American Observatory. These stars are faint, ranging in V magnitude from 13.6 in M 4 to 15.5 in M 13 and the corresponding errors in the four-color indices are ± 0.04 to 0.06 in the c1 index, for one observation. The error of the mean value of the c1 indices is approximately ± 0.02 for most of the stars since they have been measured from 4 to 10 times each.

Spectra of BHB Stars in M 3, M 13 and M 92

Spectra, at a dispersion of ∼ 50 A per millimeter, have been obtained of BHB stars in the globular clusters M 3, M 13 and M 92 with the TV scanner on the Soviet Union’s Six Meter Telescope. The spectra cover a range of 700 Angstroms in 500 channels in which counts were made of the intensity of the stellar spectrum. At this dispersion the hydrogen Balmer lines (γ, δ, e, H8 - H12) can be seen as well as the Ca II line at λ = 3934.