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Class phaser.equation.Julia

java.lang.Object
   |
   +----phaser.equation.Equation
           |
           +----phaser.equation.Julia

public class Julia

extends Equation

:          ^
: IFS(P) { C (Riemann Spherical Metric Space);
:          w[1](z) =  sqrt(z + lamda), 
:          w[2](z) = -sqrt(z + lamda) 
: }
:
: whose attractor is the Julia set:
:
:                         2
:         J[lambda](z) = z  - lamda
:
:
: NOTES for IFS implementation:
:
:    [1]  z(x,y)     = x + yi
:         lamda(a,b) = a + bi
: 
:         sqrt( z(x,y) + lamda(a,b) ) = sqrt( (x + a) + (y + b)i )
:
:    [2]  Positive square root        =     (  x[1]   +  x[2]i   )
:
:                   where
:
:                         x[1] =   sqrt( ( r + ( x + a ) ) / 2.0 )
:
:                     and if (y + b) >= 0
:
:                         x[2] =   sqrt( ( r - ( x + a ) ) / 2.0 )
:                    else x[2] =  -sqrt( ( r - ( x + a ) ) / 2.0 )
:
:                                                 2           2
:                     and    r =   sqrt( ( x + a ) + ( y + b ) )
:
:    Finally,
:             ^
:    IFS(P) { C; w[1](z), w[2](z) } as defined above maps to:
:    IFS(P) {R2; f[1](x,y) = (x[1],x[2]), f[2](x,y) = (-x[1],-x[2])}
:
:    [3]  Implement:  Apply random iteration algorithm to IFS(P),
:                     such that probability P is randomly generated:
:
:         if ( P < 0.50 ) {             // f[1](x,y) = ( x[1], x[2])
:                 x ->  x[1]
:                 y ->  x[2]
:         }
:         else {                        // f[2](x,y) = (-x[1],-x[2])
:                 x -> -x[1]
:                 y -> -x[2]
:         }
 

Julia()

eval(double[], double[], double)

 public Julia()

 public void eval(double outVector[],
                  double inVector[],
                  double time)

Overrides:

eval in class Equation

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