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，
混沌分形之填充集
。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
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// 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 = utX = yf_rand_real(-1.0f, 1.0f);
y = utY = 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)
{
utX = 0.0f;
utY = 0.0f;
}
utZ = z;
}
bool IsValidParamA() const {return true;}
bool IsValidParamB() const {return true;}
private:
int m_nIterateCount;
};
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（2）曼德勃罗集
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// 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);
utX = 0.0f;
utY = 0.0f;
float lengthSqr;
float temp;
int count = 0;
do
{
temp = outX * outX - outY * outY + cr;
utY = 2 * outX * outY + ci;
utX = temp;
lengthSqr = outX * outX + outY * outY;
count++;
}
while ((lengthSqr < 4.0f) && (count < m_nIterateCount));
if (lengthSqr < 4.0f)
{
utX = cr;
utY = ci;
}
else
{
utX = 0.0f;
utY = 0.0f;
}
utZ = 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;
};
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（3）牛顿迭代集
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// 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 = utX = yf_rand_real(-m_ParamA, m_ParamA);
y = utY = 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)
{
utX = 0.0f;
utY = 0.0f;
}
utZ = z;
}
bool IsValidParamA() const {return true;}
private:
int m_nIterateCount;
};