Julia Sets Generated By Escape Time Algorithm Is At The Application Of The Textile Pattern Design

Julia sets are the polynomial and rational function Iterative image which have been studied separately by G.Julia and P.Fatou—French mathematicians at the beginning of the 20th century.Julia images have the fine structure and the intense visual impact effects. Those as the artistic graph have a widespread application in the textile dyeing and printing, advertisement printing,industrial designining,stamp manufacture,dress designing, computer teaching research and so on.Its economic and social benefits have broad application prospects.The shape of the Julia image which has been generated by Escape Time algorithm is closely related with many parameters,such as:the limit of escape time,the limit of escape radius,the fictitious department of attraction,the radius of regional convergence and so on. Changing any of the above parameters would make Julia image changes,but so far,the relationship between the parameters and the Julia image has not been totally understood. The quick design of Julia image also has a certain barrier.Julia image has the fine structure and the layered evolution of color-effect.It tends to be used as a dyeing and printing,but as a pattern for weaving is at a constant research and exploration phase.In this paper,energy and entropy from gray level co-occurrence matrix are used to analysis the texture changes of Julia sets which are generated by the different escape time limit,escape radius limit,attraction's imaginary part and the converging-region radius.It will provide the basis for the fractal image's quick design.By the analysis,The Julia image is finer and the generated time of the image is longer,when the limit of escape time and the limit of escape radius are increasing.A general consideration,the limit of escape time is 70 and the limit of escape radius is 150.The gray level co-occurrence matrixes of the two images are transposed mutually,when the fictitious departments of attraction are inverse. The trend of each r-energy traces are same,namely r increases,the image energy reduces first,then increases,moreover flatten out,however,the r value is different when each curves achieve its minimize energy.The values of p2/q2 are different when each high time Julia images achieve its precise time. The Julia image has the fine structure and the layered evolution of color-effect.In this paper,interlacing organization's order change,miscellaneous spots are all turn into Warp interlacing point or Warp interlacing point and reasonable weft-backed renumbers are used. Julia image would have been fully demonstrated on the jacquard fabric.