GANG

home

people

projects

< previous | next >

Recall that linear GSI uses the matrix G:

This has eigenvalues d+a, d-a, with . There are 2 qualitatively different cases:

Stratification dominant: a^2>0 - a real, structures rotate no more than once with scale

Rotation dominant: a^2<0 - a imaginary, structures rotate an infinite number of times with scale.

There are 3 rotational invariants: d, a, . Hence the explorer takes f=0, r=c (other f values are obtained by rotation). Also, we fixed d=1 since it turns out that we can always replace G by G/d as long as we compensate by simultaneously taking the d power of the scale function (itself equivalent to C1->C1 d, H->H d) i.e we loose no generality with d=1 and f=0. The two main parameters we explore are thus c, e. A final parameter k allows us to examine the effect of possibly very nonroundish unit scales. In fact, we take k= log2 (r_max / r_min) where r_max, r_min are the maximum and minimum radii of the sphero-scale. k=10 thus corresponds to a unit scale which ""mixes" conventional scales (i.e. distances froom the origin, radii) over a factor of more than 1000 (2**10).

Here we explore this 3 dimensional parameter space with i=c, j=e. Since at each point a 2D image is necessary to understand how the parameters interact, we present the data in 2D cross sections, with each of i,j and k held constant separately.

CLICK ON A PLANE TO CHOOSE i (GSI parameter c):

CLICK ON A PLANE TO CHOOSE j (GSI parameter e):

CLICK ON A PLANE TO CHOOSE k (anisotropy of the unit ball parameter):

< previous | next >