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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

混沌分形之逻辑斯蒂(Logistic)映射系统