Fractal structure of the Horsehead nebula (B 33)

Department of Applied Mathematics, University of Calcutta, 92 APC Road, Calcutta 700 009, India

Corresponding author: srabani@cucc.ernet.in

Received: 6 December 2001
Accepted: 5 September 2002

Abstract

Analysis of the CCD image of the Horsehead nebula (B 33), taken in the H α (6561 Å) using the 2.34 m Vainu Bappu Telescope (VBT) at Kavalur, India, is performed to test its fractal structure. Ten sample readings of the box dimension of this image were taken using a fractal analysis software, giving an average value of 1.6965725. The sample dimensions were found to be different from the topological dimension of one. Importantly, the box dimension of B 33 was not found to be significantly different from that of the Julia set (box dimension 1.679594) with c = -0.745429 + 0.113008i. This provides compelling evidence to show that the structure of the Horsehead nebula is not only fractal, but also that its geometry can be described by the Julia function  = z² + c, where both z and c are complex numbers.