31 Astrophysics, Vol. 59, No. 1, March , 2016 0571-7256/16/5901-0031 © 2016 Springer Science+Business Media New York Original article submitted October 10, 2015; accepted for publication December 16, 2015. Translated from Astrofizika, Vol. 59, No. 1, pp. 35-42 (February 2016). FRACTALITY OF ISOTHERMS OF THE COSMIC MICROWAVE BACKGROUND BASED ON DATA FROM THE PLANCK SPACECRAFT A. A. Mylläri, 1 A. A. Raikov, 2 V. V. Orlov, 2,3 P. A. Tarakanov, 3 V. N. Yershov, 2,4 and M. Y. Yezhkov 3 A system of isophotes of the cosmic microwave background (CMB) is constructed for several regions on the celestial sphere using data from the Planck spacecraft. The fractal dimensionality of the isotherms is estimated to be 03 0 78 1 . . D c   . Our results agree with earlier work based on the ILC charts with WMAP data. Our simulations confirm the previous conclusion that a similar dimensionality is obtained for a gaussian spectrum of initial perturbations. Keywords: microwave background radiation: maps of isotherms: fractality 1. Introduction The first complete survey of the sky with instruments mounted on board of the Planck spacecraft [1] yielded a number of important scientific results (catalogs of radiation sources, charts of the distributions of gas and dust, etc.). One of the major results is a chart of the fluctuations in the cosmic microwave background (CMB). The sky survey was conducted in nine frequency bands (30, 44, 70, 100, 143, 217, 353, 545, and 857 GHz) with two instruments on the Planck satellite. The result was a chart of the distribution of the sources of the forward background, which (1) St. Georges University, St. Georges, Grenada (2) Main (Pulkovo) Astronomical Observatory, Russian Academy of Sciences, St. Petersburg, Russia; e-mail: vorvor1956@yandex.ru (3) St. Petersburg State University, St. Petersburg, Russia (4) Mullard Space Science Laboratory, University College of London, Dorking, United Kingdom DOI 10.1007/s10511-016-9413-1