Others attractors...


Various types of attractors with trigonometric functions



Pickover
default values

SinCos, Pickover and KingsDream

Various types of attractors with trigonometric functions

3D attractors are point clouds generate from sequences of numbers pn{xn,yn,zn} ⇒ pnR3, nN, where n0→∞ denotes the step of the iteration process starting from a initial p0{x0,y0,z0} point.
In the cloud each next point is function of the previous one:

\[ \eqalign { x_{i+1} = \xi(x_i, y_i, z_i) & \\ y_{i+1} = \phi(x_i, y_i, z_i) & \\ z_{i+1} = \psi(x_i, y_i, z_i) & } \qquad \Bigg\{ \eqalign { & x, y, z \in R \\ & [0, i, n_{\rightarrow\infty}[ \text{   } \Rightarrow i,n \in N \\ } \]


In the computational code:


 

In the ATTRACTORS window of glChAoS.P:


Colors are indicative of point speed: distance between pi and pi+1
 
You can to start wglChAoS.P with a specific attractor directly from  explore  button. Select lowResources for low resources devices (e.g. mobile devices)
 

Resolution: X        fixed canvas
 
  touchScreen         lowResources

 

 

\begin{align} x_{i+1} & = sin(k_0 \centerdot y_i) + z_i \centerdot cos(k_1 \centerdot x_i) \\ y_{i+1} & = z_i \centerdot sin(k_2 \centerdot x_i) - cos(k_3 \centerdot y_i) \\ z_{i+1} & = sin( x_i)\\ \end{align}

 

explore
    pNew.x =     sin(kVal[0]*p.y) - p.z*cos(kVal[1]*p.x);
    pNew.y = p.z*sin(kVal[2]*p.x) -     cos(kVal[3]*p.y);
    pNew.z =     sin(p.x)                               ;

\begin{align} x_{i+1} & = & cos(k_0 \centerdot x_i) + sin(k_1 \centerdot y_i) - sin(k_2 \centerdot z) \\ y_{i+1} & = & sin(k_3 \centerdot x_i) - cos(k_4 \centerdot y_i) + sin(k_5 \centerdot z) \\ z_{i+1} & = & -cos(k_6 \centerdot x_i) + cos(k_7 \centerdot y_i) + cos(k_8 \centerdot z) \\ \end{align}

 

explore
    pNew.x =  cos(kVal[0]*p.x) + sin(kVal[1]*p.y) - sin(kVal[2]*p.z);
    pNew.y =  sin(kVal[3]*p.x) - cos(kVal[4]*p.y) + sin(kVal[5]*p.z);
    pNew.z = -cos(kVal[6]*p.x) + cos(kVal[7]*p.y) + cos(kVal[8]*p.z);

\begin{align} x_{i+1} & = sin(z_i \centerdot k_0) + k_3 \centerdot sin(x_i \centerdot k_0) \\ y_{i+1} & = sin(x_i \centerdot k_1) + k_4 \centerdot sin(y_i \centerdot k_1) \\ z_{i+1} & = sin(y_i \centerdot k_2) + k_5 \centerdot sin(z_i \centerdot k_2) \\ \end{align}

 

explore
    pNew.x = sin(p.z * kVal[0]) + kVal[3] * sin(p.x * kVal[0]);
    pNew.y = sin(p.x * kVal[1]) + kVal[4] * sin(p.y * kVal[1]);
    pNew.z = sin(p.y * kVal[2]) + kVal[5] * sin(p.z * kVal[2]);