Faster Fractal Pictures Using Optimal Sequences

McFarlane, Isobel (1993) Faster Fractal Pictures Using Optimal Sequences. PhD thesis, University of Glasgow.

Abstract

Today a wide variety of images may be expressed as the attractor A of an iterated function system in the plane. An iterated function system or IFS is a finite collection of affine transformations w1,..., WN, while the attractor A is the unique fixed point of the associated collage map W where W(E) =UiWi(E) for any compact set E [4]. Since only 6N real numbers, known as the code of the IFS, are necessary to store this image, IFS's are being considered as a method of image compression [2, 5]. Moreover, algorithms which produce A quickly on a computer screen are being sought. In this thesis, we study combinatorial ways of screening fractal pictures from the IFS code. We introduce the optimal sequence method and show it to be more accurate and faster than the widely used Random Iteration Algorithm (RIA for short) [1, 4, 16]. We also show it to be superior to the Adaptive Cut Method or ACM [13, 28] - one of the best non-RIA algorithms. For uniform IFS, our investigations also lead to the expansion of the term M- sequence to include linear recurring sequences of period Nk-1 over structures other than finite fields, and in particular over far rings which we define. We also study a new class of latin squares - k-recurrent latin squares. For non-uniform IFS, we initially restrict ourselves to a very simple model before extending the results obtained to more complicated models.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: Stuart G Hoggar
• Keywords: Applied mathematics, Computer science
• Date of Award: 1993
• Depositing User: Enlighten Team
• Unique ID: glathesis:1993-76432
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 19 Nov 2019 14:21
• Last Modified: 19 Nov 2019 14:21
• URI: https://theses.gla.ac.uk/id/eprint/76432