混沌分形之填充集

通过分形来生成图像，有一个特点是：不想生成什么样的图像就写出相应的算法，而是生成出来的图像像什么，那算法就是什么。总之，当你在写这个算法时或设置相关参数时，你几乎无法猜测出你要生成的图像是什么样子。而生成图像的时间又比较久，无法实时地调整参数。所以我这使用了填充集的方式，先计算少量的顶点，以显示出图像的大致轮廓。确定好参数后再进行图像生成。所谓填充集，就是随机生成顶点位置，当满足要求时顶点保留，否则剔除。这里将填充集的方式来生成Julia集，曼德勃罗集和牛顿迭代集.

（1）Julia集

// 填充Julia集 // http://www.douban.com/note/230496472/ class JuliaSet2 : public FractalEquation { public: JuliaSet2() { m_StartX = 0.0f; m_StartY = 0.0f; m_StartZ = 0.0f; m_ParamA = 0.11f; m_ParamB = 0.615f; m_nIterateCount = 80; } void IterateValue(float x, float y, float z, float& outX, float& outY, float& outZ) const { x = outX = yf_rand_real(-1.0f, 1.0f); y = outY = yf_rand_real(-1.0f, 1.0f); float lengthSqr; float temp; int count = 0; do { temp = x * x - y * y + m_ParamA; y = 2 * x * y + m_ParamB; x = temp; lengthSqr = x * x + y * y; count++; } while ((lengthSqr < 4.0f) && (count < m_nIterateCount)); if (lengthSqr > 4.0f) { outX = 0.0f; outY = 0.0f; } outZ = z; } bool IsValidParamA() const {return true;} bool IsValidParamB() const {return true;} private: int m_nIterateCount; };

（2）曼德勃罗集

// 曼德勃罗集 // http://www.cnblogs.com/Ninputer/archive/2009/11/24/1609364.html class MandelbrotSet : public FractalEquation { public: MandelbrotSet() { m_StartX = 0.0f; m_StartY = 0.0f; m_StartZ = 0.0f; m_ParamA = -1.5f; m_ParamB = 1.0f; m_ParamC = -1.0f; m_ParamD = 1.0f; m_nIterateCount = 100; } void IterateValue(float x, float y, float z, float& outX, float& outY, float& outZ) const { float cr = m_ParamA + (m_ParamB - m_ParamA)*((float)rand()/RAND_MAX); float ci = m_ParamC + (m_ParamD - m_ParamC)*((float)rand()/RAND_MAX); outX = 0.0f; outY = 0.0f; float lengthSqr; float temp; int count = 0; do { temp = outX * outX - outY * outY + cr; outY = 2 * outX * outY + ci; outX = temp; lengthSqr = outX * outX + outY * outY; count++; } while ((lengthSqr < 4.0f) && (count < m_nIterateCount)); if (lengthSqr < 4.0f) { outX = cr; outY = ci; } else { outX = 0.0f; outY = 0.0f; } outZ = z; } bool IsValidParamA() const {return true;} bool IsValidParamB() const {return true;} bool IsValidParamC() const {return true;} bool IsValidParamD() const {return true;} private: int m_nIterateCount; };

（3）牛顿迭代集

// 牛顿迭代 // http://www.douban.com/note/230496472/ class NewtonIterate : public FractalEquation { public: NewtonIterate() { m_StartX = 0.0f; m_StartY = 0.0f; m_StartZ = 0.0f; m_ParamA = 1.0f; m_nIterateCount = 64; } void IterateValue(float x, float y, float z, float& outX, float& outY, float& outZ) const { x = outX = yf_rand_real(-m_ParamA, m_ParamA); y = outY = yf_rand_real(-m_ParamA, m_ParamA); float xx, yy, d, tmp; for (int i = 0; i < m_nIterateCount; i++) { xx = x*x; yy = y*y; d = 3.0f*((xx - yy)*(xx - yy) + 4.0f*xx*yy); if (fabsf(d) < EPSILON) { d = d > 0.0f ? EPSILON : -EPSILON; } tmp = x; x = 0.666667f*x + (xx - yy)/d; y = 0.666667f*y - 2.0f*tmp*y/d; } if (x < 0.0f) { outX = 0.0f; outY = 0.0f; } outZ = z; } bool IsValidParamA() const {return true;} private: int m_nIterateCount; };

（4）

关于基类FractalEquation的定义见：混沌与分形

再发几幅图像：







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