混沌分形之逻辑斯蒂（Logistic）映射系统

前几天，有个同事看到我生成的一幅逻辑斯蒂分岔图像后，问我：“这是咪咪吗?”我回答：“淫者见淫。”好吧，这里将生成几种分岔映射图形，包括逻辑斯蒂映射系统，正弦映射系统和曼德勃罗映射系统。实际上这几种图形算不上分形，只不过它与我写的其他分形对象使用相同的基类，所以也将其列入混沌分形的范畴。

关于基类FractalEquation的定义及相关软件见：混沌与分形

（1）逻辑斯蒂映射系统

// 逻辑斯蒂映射系统 class LogisticMap : public FractalEquation { public: LogisticMap() { m_StartX = 0.0f; m_StartY = 0.0f; m_StartZ = 0.0f; m_ParamA = 0.0f; m_ParamB = 4.0f; m_nIterateCount = 100; } void IterateValue(float x, float y, float z, float& outX, float& outY, float& outZ) const { float R = (float)rand()/RAND_MAX; float k = m_ParamA + (m_ParamB - m_ParamA) * R; outX = R*4.0f; outY = (float)rand()/RAND_MAX; for (int i = 0; i < m_nIterateCount; i++) { outY = k*outY*(1-outY); } outY *= 2; outZ = z; } bool IsValidParamA() const {return true;} bool IsValidParamB() const {return true;} private: int m_nIterateCount; };

调节下参数后的图形：



（2）正弦映射系统

// 正弦映射系统 class SinMap : public FractalEquation { public: SinMap() { m_StartX = 0.0f; m_StartY = 0.0f; m_StartZ = 0.0f; m_ParamA = -2*PI; m_ParamB = 2*PI; m_nIterateCount = 64; } void IterateValue(float x, float y, float z, float& outX, float& outY, float& outZ) const { float R = (float)rand()/RAND_MAX; float k = m_ParamA + (m_ParamB - m_ParamA) * R; outX = R*4.0f; outY = (float)rand()/RAND_MAX; for (int i = 0; i < m_nIterateCount; i++) { outY = k*sinf(outY); } outY *= 0.5f; outZ = z; } bool IsValidParamA() const {return true;} bool IsValidParamB() const {return true;} private: int m_nIterateCount; };

（3）曼德勃罗映射系统

// 曼德勃罗映射系统 class MandelbrotMap : public FractalEquation { public: MandelbrotMap() { m_StartX = 0.0f; m_StartY = 0.0f; m_StartZ = 0.0f; m_ParamA = -2.0f; m_ParamB = 0.0f; m_nIterateCount = 64; } void IterateValue(float x, float y, float z, float& outX, float& outY, float& outZ) const { float R = (float)rand()/RAND_MAX; float k = m_ParamA + (m_ParamB - m_ParamA) * R; outX = R*4.0f; outY = (float)rand()/RAND_MAX; for (int i = 0; i < m_nIterateCount; i++) { outY = outY*outY + k; } outZ = z; } bool IsValidParamA() const {return true;} bool IsValidParamB() const {return true;} private: int m_nIterateCount; };

最后发下被我同事当成MM的逻辑斯蒂分岔图像：



之前我还写过一篇关于逻辑斯蒂的文章：混沌数学之logistic模型