本文選題：混沌函數(shù)　切入點(diǎn)：PSO　出處：《山東師范大學(xué)》2013年碩士論文

【摘要】：分形理論是幾何學(xué)的一個(gè)新的研究方向——分形幾何學(xué)，因?yàn)槠淠軌蚝芎玫哪M自然景物，又名大自然的幾何學(xué)。除了具有普通藝術(shù)圖案的特點(diǎn)之外，，分形圖形一般具有自相似性和無限的精細(xì)結(jié)構(gòu)等特征。分形與混沌分別在空間和時(shí)間標(biāo)度下表現(xiàn)出自相似性�？梢哉f，混沌與分形具有內(nèi)在的本質(zhì)聯(lián)系。目前，混沌分形圖已經(jīng)被廣泛應(yīng)用于商標(biāo)防偽、紡織和科幻影片等之中，在圖案設(shè)計(jì)中占有獨(dú)特的地位。 混沌現(xiàn)象是大千世界中存在的一種復(fù)雜的物理現(xiàn)象，是非線性動力系統(tǒng)的固有特性�；煦缥邮怯苫煦绾瘮�(shù)反復(fù)迭代而成，由無窮多個(gè)迭代點(diǎn)集組成，是混沌現(xiàn)象的一種“圖形化”描述。這種圖形具有明顯的分形特征，也常被稱為混沌分形圖。有一類混沌分形圖不僅具有混沌現(xiàn)象，還具有大量內(nèi)置的對稱現(xiàn)象。 本文研究的內(nèi)容主要是針對具有對稱現(xiàn)象的混沌分形圖，主要包括三個(gè)方面：利用PSO實(shí)現(xiàn)混沌吸引子參數(shù)的快速優(yōu)化，提出基于色彩控制圓的渲染方案，圖形參數(shù)的控制及圖形的繪制。首先，利用計(jì)算機(jī)豐富的顯示功能，實(shí)現(xiàn)對對稱分形圖在周期、位置、大小、色彩上的參數(shù)可控，使普通用戶可通過對話框方便地生成各類對稱分形圖；在此研究的基礎(chǔ)上，提出一種改進(jìn)的配色方案——基于色彩控制圓的渲染方案，可使圖案視覺效果由簡單變化到絢麗多彩；最終對某個(gè)特定的混沌函數(shù)系統(tǒng)編程實(shí)現(xiàn)一個(gè)產(chǎn)生對稱性混沌分形圖的模擬系統(tǒng)。按實(shí)際的實(shí)施過程，具體的研究內(nèi)容如下： (1)利用PSO優(yōu)化對稱分形圖的參數(shù)向量 本項(xiàng)研究將PSO應(yīng)用于優(yōu)化混沌吸引子參數(shù)向量的問題，構(gòu)造了特定混沌函數(shù)參數(shù)向量作為粒子表達(dá)方法，建立了此問題的PSO。試驗(yàn)結(jié)果表明，PSO可以快速、高效求得各參數(shù)向量的最優(yōu)解，從而解決了在巨大參數(shù)空間下生成混沌分形圖困難的問題。 (2)確定渲染方案 本文結(jié)合對稱分形圖的特點(diǎn)，以敦煌飛天圖的色彩組合為基調(diào)，提出了一種以藍(lán)、紫、紅、黃為主色調(diào)的渲染方法，表現(xiàn)出一種似夢似真飄渺虛幻靈動彌漫的感染力。 (3)對稱分形圖的參數(shù)可控性研究 查閱大量的參考文獻(xiàn)，研究對稱分形圖的生成原理及方法。本文以帶群p1a1模型為例，通過對其生成原理、繪制方法、渲染方案進(jìn)行研究，提煉出可控參數(shù)。普通用戶通過對話框方便的控制這些參數(shù)，從而生成用戶滿意的對稱分形圖案。 (4)模擬系統(tǒng)的開發(fā) 開發(fā)了一個(gè)簡單實(shí)用的模擬系統(tǒng)，實(shí)現(xiàn)了對稱分形圖的參數(shù)的優(yōu)化、及圖案的繪制與保存，設(shè)計(jì)較為方便的顏色對話框，用戶可通過指定調(diào)色板中的色彩來設(shè)置分形圖案的主色調(diào)，為用戶提供了簡單易操作的系統(tǒng)界面，同時(shí)為后續(xù)的研究提供了便捷工具。 本文所生成的對稱分形圖呈現(xiàn)的空間結(jié)構(gòu)精細(xì)、形態(tài)瑰麗、內(nèi)涵豐富，不僅具有豐厚的理論意義，而且可廣泛應(yīng)用于社會生活中的圖案設(shè)計(jì)，有望在紡織、印刷、廣告、防偽等圖案設(shè)計(jì)領(lǐng)域引起關(guān)注。
[Abstract]:Fractal theory is a new research direction of geometry - fractal geometry, because of its natural scenery simulation can be very good, also known as the geometry of nature. In addition to having features of ordinary art patterns, fractal graphics generally have self similarity and unlimited fine structure feature. Fractal and chaos in space and time scale under the self similarity characteristic. It can be said that the chaos and fractal are internally related. At present, the chaotic fractal graph has been widely used in trademarks, textile and other science fiction films, the pattern design has a unique position.
Chaos is a kind of complex physical phenomena exist in the universe of 1,000,000,000 universes are inherent in the nonlinear dynamic system. The chaotic attractor is a chaotic function iteratively and, by an infinite number of iteration point set, is a "graphic" description of the chaotic phenomenon. This figure has obvious fractal characteristics, also often referred to as the chaos and fractal graph. A kind of chaos and fractal graph not only has chaotic phenomenon, also has a large number of built-in symmetricphenomenon.
The content of this paper is mainly based on chaotic fractal images with symmetrical phenomenon, mainly includes three aspects: to realize rapid optimization of chaotic attractor parameters by using PSO, the rendering scheme based on color control circle, drawing graphics and control parameters. First, the use of computer display, to achieve symmetric fractal graph in the period, location, size, color parameters, which can be conveniently through the dialog box to generate various types of symmetrical fractal figure of ordinary users; on the basis of this study, this paper proposes an improved color scheme - rendering scheme based on color control circle, which can make the design of visual effects by a simple change to achieve a bright and colorful; have the symmetry of chaos and fractal graph simulation system for a particular programming iteration function system. According to the actual implementation process, the specific research contents as follows:
(1) the parameter vector using PSO optimization symmetrical fractal figure
This study applies PSO to optimize the parameter of chaotic attractor vector, constructed the specific chaotic function parameter vector as the particle expression method, established the PSO. test results of this problem shows that PSO can quickly and efficiently obtain the optimal parameters of vector solution, so as to solve the difficulty of generating chaotic fractal graph under huge parameter space the problem.
(2)紜畾娓叉煋鏂規(guī)
In this paper, combined with the characteristics of symmetrical fractal figure, Dunhuang flying figure color combinations for the tone, presents a blue, purple, red, yellow color rendering method, showing a dream likereally misty illusory facial diffuse appeal.
(3) the controllable parameters about the symmetrical fractal figure
Access to a large number of references, the generation principle and method of the symmetrical fractal figure. This thesis takes p1a1 model as an example, the generation principle of the method of drawing, rendering research plan, refine controllable parameters. Ordinary users to control these parameters through the dialog box is convenient, so as to generate symmetrical fractal patterns of user satisfaction.
(4) the development of simulation system
The development of a simple and practical simulation system, realize the optimization of parameters of symmetrical fractal figure, and pattern drawing and preservation, design more convenient color dialog box, the user can set the main tone of fractal pattern by specifying the palette color, provides the interface of the system is simple and easy to operate for the users, while providing a convenient tool for the follow-up study.
The spatial structure of the symmetrical fractal figure generated by the present form of fine, magnificent, rich in content, not only has theoretical significance but also rich, can be widely used in the social life of the design, is expected in the textile, printing, advertising, has attracted the attention of security and other design fields.

【學(xué)位授予單位】：山東師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：TP391.41;O189

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