Families of Self-Similar Symmetric Laplacians on the Interval and Sierpinski Gasket
Eigenfunctions
For the interval, the PDFs below contain plots of all of the eigenfunctions for the given parameters. For SG, the zipped files contain MATLAB figures of all the eigenfunctions for the given parameters.

For the threshold division scheme, the cutoff values are determined in the following way. We take the two measure parameters, and choose 4 evenly spaced points between the values, excluding the smaller measure parameter and including the larger measure parameter. They are numbered in increasing order.
Eigenfunctions on the Interval
p m=1 m=2 m=3 m=4
0.1 PDF PDF PDF PDF
0.2 PDF PDF PDF PDF
0.3 PDF PDF PDF PDF
0.4 PDF PDF PDF PDF
0.49 PDF PDF PDF PDF
0.5 PDF PDF PDF PDF
0.51 PDF PDF PDF PDF
0.6 PDF PDF PDF PDF
0.7 PDF PDF PDF PDF
0.8 PDF PDF PDF PDF
0.9 PDF PDF PDF PDF
Eigenfunctions on the Gasket
r m=1 m=2 m=3
1 Zip Zip Zip
twin(1) Zip Zip Zip
max (0.64) Zip Zip Zip
0.6 Zip Zip Zip
twin(0.6) Zip Zip Zip
0.5 Zip Zip Zip
twin(0.5) Zip Zip Zip
0.4 Zip Zip Zip
twin(0.4) Zip Zip Zip
0.3 Zip Zip Zip
twin(0.3) Zip Zip Zip
0.2 Zip Zip Zip
twin(0.2) Zip Zip Zip
0.1 Zip Zip Zip
twin(0.1) Zip Zip Zip
Eigenfunctions on the gasket with threshold division
Cutoff #1
r m=1 m=2 m=3
1 Zip Zip Zip
twin(1) Zip Zip Zip
max (0.64) Zip Zip Zip
0.6 Zip Zip Zip
twin(0.6) Zip Zip Zip
0.5 Zip Zip Zip
twin(0.5) Zip Zip Zip
0.4 Zip Zip Zip
twin(0.4) Zip Zip Zip
0.3 Zip Zip Zip
twin(0.3) Zip Zip Zip
0.2 Zip Zip Zip
twin(0.2) Zip Zip Zip
0.1 Zip Zip Zip
twin(0.1) Zip Zip Zip
Cutoff #2
r m=1 m=2 m=3
1 Zip Zip Zip
twin(1) Zip Zip Zip
max (0.64) Zip Zip Zip
0.6 Zip Zip Zip
twin(0.6) Zip Zip Zip
0.5 Zip Zip Zip
twin(0.5) Zip Zip Zip
0.4 Zip Zip Zip
twin(0.4) Zip Zip Zip
0.3 Zip Zip Zip
twin(0.3) Zip Zip Zip
0.2 Zip Zip Zip
twin(0.2) Zip Zip Zip
0.1 Zip Zip Zip
twin(0.1) Zip Zip Zip
Cutoff #3
r m=1 m=2 m=3
1 Zip Zip Zip
twin(1) Zip Zip Zip
max (0.64) Zip Zip Zip
0.6 Zip Zip Zip
twin(0.6) Zip Zip Zip
0.5 Zip Zip Zip
twin(0.5) Zip Zip Zip
0.4 Zip Zip Zip
twin(0.4) Zip Zip Zip
0.3 Zip Zip Zip
twin(0.3) Zip Zip Zip
0.2 Zip Zip Zip
twin(0.2) Zip Zip Zip
0.1 Zip Zip Zip
twin(0.1) Zip Zip Zip
Cutoff #4
r m=1 m=2 m=3
1 Zip Zip Zip
twin(1) Zip Zip Zip
max (0.64) Zip Zip Zip
0.6 Zip Zip Zip
twin(0.6) Zip Zip Zip
0.5 Zip Zip Zip
twin(0.5) Zip Zip Zip
0.4 Zip Zip Zip
twin(0.4) Zip Zip Zip
0.3 Zip Zip Zip
twin(0.3) Zip Zip Zip
0.2 Zip Zip Zip
twin(0.2) Zip Zip Zip
0.1 Zip Zip Zip
twin(0.1) Zip Zip Zip
Eigenfunctions on the interval with threshold division
Cutoff #1
p m=1 m=2 m=3 m=4
0.1 PDF PDF PDF PDF
0.2 PDF PDF PDF PDF
0.3 PDF PDF PDF PDF
0.4 PDF PDF PDF PDF
0.49 PDF PDF PDF PDF
0.5 PDF PDF PDF PDF
0.51 PDF PDF PDF PDF
0.6 PDF PDF PDF PDF
0.7 PDF PDF PDF PDF
0.8 PDF PDF PDF PDF
0.9 PDF PDF PDF PDF
Cutoff #2
p m=1 m=2 m=3 m=4
0.1 PDF PDF PDF PDF
0.2 PDF PDF PDF PDF
0.3 PDF PDF PDF PDF
0.4 PDF PDF PDF PDF
0.49 PDF PDF PDF PDF
0.5 PDF PDF PDF PDF
0.51 PDF PDF PDF PDF
0.6 PDF PDF PDF PDF
0.7 PDF PDF PDF PDF
0.8 PDF PDF PDF PDF
0.9 PDF PDF PDF PDF
Cutoff #3
p m=1 m=2 m=3 m=4
0.1 PDF PDF PDF PDF
0.2 PDF PDF PDF PDF
0.3 PDF PDF PDF PDF
0.4 PDF PDF PDF PDF
0.49 PDF PDF PDF PDF
0.5 PDF PDF PDF PDF
0.51 PDF PDF PDF PDF
0.6 PDF PDF PDF PDF
0.7 PDF PDF PDF PDF
0.8 PDF PDF PDF PDF
0.9 PDF PDF PDF PDF
Cutoff #4
p m=1 m=2 m=3 m=4
0.1 PDF PDF PDF PDF
0.2 PDF PDF PDF PDF
0.3 PDF PDF PDF PDF
0.4 PDF PDF PDF PDF
0.49 PDF PDF PDF PDF
0.5 PDF PDF PDF PDF
0.51 PDF PDF PDF PDF
0.6 PDF PDF PDF PDF
0.7 PDF PDF PDF PDF
0.8 PDF PDF PDF PDF
0.9 PDF PDF PDF PDF