Fractal images from z <- za + c in the complex c-plane
| dc.contributor.author | Gujar, Uday, G. | |
| dc.contributor.author | Bhavsar, Virendra, C. | |
| dc.date.accessioned | 2023-03-01T18:28:54Z | |
| dc.date.available | 2023-03-01T18:28:54Z | |
| dc.date.issued | 1988 | |
| dc.description.abstract | In this paper, we propose the generalized transformation function z <- z[superscript a] + c for generating fractal images. The self-squared function z <- z[superscript 2] + c, which is discussed extensively in the literature, is a special case of this function. A multitude of interesting, intriguing and rich families of fractals are generated by changing a single parameter, a. Direct relationships are observed between a and the visual characteristics of the fractal image in the c-plane. The exponent a can be represented as a = +-(n+e), where n and e are the integer and fractional parts, respectively. It is found that when a is a positive integer number, the resulting image contains lobular structures. The number of major lobes equals (n-1). When a is a negative integer number, the generated fractal image is a planetary structure consisting of overlapping central planets surrounded by satellite structures. The number of satellite structures equals (n+1). A continuous variation of a between two consecutive integers results into a continuous proportional change between the two limiting fractal images. Several conjectures about the visual characteristics of the images and the value of a are stated. | |
| dc.description.copyright | Copyright @ Uday G. Gujar and Virendra C. Bhavsar, 1988. | |
| dc.identifier.uri | https://unbscholar.lib.unb.ca/handle/1882/14884 | |
| dc.rights | http://purl.org/coar/access_right/c_abf2 | |
| dc.subject.discipline | Computer Science | |
| dc.title | Fractal images from z <- za + c in the complex c-plane | |
| dc.type | technical report |
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