A Method to Solve the Limitations in Drawing External Rays of the Mandelbrot Set. (24th September 2013)

• Record Type: Journal Article
• Authors: Romera, M.; Pastor, G.; Orue, A. B.; Martin, A.; Danca, M.-F.; Montoya, F.
• Other Names: Chen Guanrong (Ron) Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-09-24
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/105283
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : The external rays of the Mandelbrot set are a valuable graphic tool in order to study this set. They are drawn using computer programs starting from the Böttcher coordinate. However, the drawing of an external ray cannot be completed because it reaches a point from which the drawing tool cannot continue drawing. This point is influenced by the resolution of the standard for floating-point computation used by the drawing program. The IEEE 754 Standard for Floating-Point Arithmetic is the most widely used standard for floating-point computation, and we analyze the possibilities of the quadruple 128 bits format of the current IEEE 754-2008 Standard in order to draw external rays. When the drawing is not possible, due to a lack of resolution of this standard, we introduce a method to draw external rays based on the escape lines and Bézier curves.