static void
Random_Prm(DBL * Prm)
{
int i;
for (i = 0; i < MAX_PRM; ++i)
Prm[i] = Gauss_Rand(Mid_Prm[i], Amp_Prm[i], 4.0);
}
/* Sets up initial conditions for a flow without all the extra baggage
that goes with init_flow */
static void
restart_flow(ModeInfo * mi)
{
flowstruct *sp;
int b;
if (flows == NULL)
return;
sp = &flows[MI_SCREEN(mi)];
sp->count = 0;
/* Re-Initialize point positions, velocities, etc. */
for (b = 0; b < sp->beecount; b++) {
X(0, b) = Gauss_Rand(sp->range.x);
Y(0, b) = (sp->yperiod > 0)?
balance_rand(sp->range.y) : Gauss_Rand(sp->range.y);
Z(0, b) = Gauss_Rand(sp->range.z);
}
}
static Bool
discover(ModeInfo * mi)
{
flowstruct *sp;
double l = 0;
dvector dl;
dvector max, min;
double dl2, df, rs, lsum = 0, s, maxv2 = 0, v2;
int N, i, nl = 0;
if (flows == NULL)
return 0;
sp = &flows[MI_SCREEN(mi)];
if(sp->count2 == 0) {
/* initial conditions */
sp->p2[0].x = Gauss_Rand(sp->range.x);
sp->p2[0].y = (sp->yperiod > 0)?
balance_rand(sp->range.y) : Gauss_Rand(sp->range.y);
sp->p2[0].z = Gauss_Rand(sp->range.z);
/* 1000 steps to find an attractor */
/* Most cases explode out here */
for(N=0; N < 1000; N++){
Iterate(sp->p2, sp->ODE, sp->par2, sp->step2);
if(sp->yperiod > 0 && sp->p2[0].y > sp->yperiod)
sp->p2[0].y -= sp->yperiod;
if(fabs(sp->p2[0].x) > LOST_IN_SPACE ||
fabs(sp->p2[0].y) > LOST_IN_SPACE ||
fabs(sp->p2[0].z) > LOST_IN_SPACE) {
return 0;
}
sp->count2++;
}
/* Small perturbation */
sp->p2[1].x = sp->p2[0].x + 0.000001;
sp->p2[1].y = sp->p2[0].y;
sp->p2[1].z = sp->p2[0].z;
}
/* Reset bounding box */
max.x = min.x = sp->p2[0].x;
max.y = min.y = sp->p2[0].y;
max.z = min.z = sp->p2[0].z;
/* Compute Lyapunov Exponent */
/* (Technically, we're only estimating the largest Lyapunov
Exponent, but that's all we need to know to determine if we
have a strange attractor.) [TDA] */
/* Fly two bees close together */
for(N=0; N < 5000; N++){
for(i=0; i< 2; i++) {
v2 = Iterate(sp->p2+i, sp->ODE, sp->par2, sp->step2);
if(sp->yperiod > 0 && sp->p2[i].y > sp->yperiod)
sp->p2[i].y -= sp->yperiod;
if(fabs(sp->p2[i].x) > LOST_IN_SPACE ||
fabs(sp->p2[i].y) > LOST_IN_SPACE ||
fabs(sp->p2[i].z) > LOST_IN_SPACE) {
return 0;
}
if(v2 > maxv2) maxv2 = v2; /* Track max v^2 */
}
/* find bounding box */
if ( sp->p2[0].x < min.x ) min.x = sp->p2[0].x;
else if ( sp->p2[0].x > max.x ) max.x = sp->p2[0].x;
if ( sp->p2[0].y < min.y ) min.y = sp->p2[0].y;
else if ( sp->p2[0].y > max.y ) max.y = sp->p2[0].y;
if ( sp->p2[0].z < min.z ) min.z = sp->p2[0].z;
else if ( sp->p2[0].z > max.z ) max.z = sp->p2[0].z;
/* Measure how much we have to pull the two bees to prevent
them diverging. */
dl.x = sp->p2[1].x - sp->p2[0].x;
dl.y = sp->p2[1].y - sp->p2[0].y;
dl.z = sp->p2[1].z - sp->p2[0].z;
dl2 = dl.x*dl.x + dl.y*dl.y + dl.z*dl.z;
if(dl2 > 0) {
df = 1e12 * dl2;
rs = 1/sqrt(df);
sp->p2[1].x = sp->p2[0].x + rs * dl.x;
sp->p2[1].y = sp->p2[0].y + rs * dl.y;
sp->p2[1].z = sp->p2[0].z + rs * dl.z;
lsum = lsum + log(df);
nl = nl + 1;
l = M_LOG2E / 2 * lsum / nl / sp->step2;
}
sp->count2++;
}
/* Anything that didn't explode has a finite attractor */
/* If Lyapunov is negative then it probably hit a fixed point or a
* limit cycle. Positive Lyapunov indicates a strange attractor. */
sp->lyap2 = l;
sp->size2 = max.x - min.x;
s = max.y - min.y;
if(s > sp->size2) sp->size2 = s;
s = max.z - min.z;
if(s > sp->size2) sp->size2 = s;
sp->mid2.x = (max.x + min.x) / 2;
sp->mid2.y = (max.y + min.y) / 2;
sp->mid2.z = (max.z + min.z) / 2;
if(sqrt(maxv2) > sp->size2 * 0.2) {
/* Flowing too fast, reduce step size. This
helps to eliminate high-speed limit cycles,
which can show +ve Lyapunov due to integration
inaccuracy. */
sp->step2 /= 2;
}
return 1;
}
