Julia Sets
Computation of the Area (Iter. 170)
Image size 5120x3840:
Data
Slice at Im(c)=0
Image size 640x480:
Data
2D
3D
Computation of the Box-Counting Dimension (Iter. 170)
Data:
Rectangle
Slice at Im(c)=0
Slice at Re(c)=-0.12
Graphs:
Slice at Im(c)=0
(Zoom)
Slice at Re(c)=-0.12
Power Law (Log-Log)
2D Full
3D Full
Eigenvalues with Dirichlet boundary conditions (Iter. 170, Res. 200)
-0.50+0.00i
-0.50+0.05i
-0.50+0.10i
-0.50+0.15i
-0.50+0.20i
-0.50+0.25i
-0.50+0.30i
-0.50+0.35i
-0.50+0.40i
-0.50+0.45i
-0.45+0.00i
-0.45+0.05i
-0.45+0.10i
-0.45+0.15i
-0.45+0.20i
-0.45+0.25i
-0.45+0.30i
-0.45+0.35i
-0.45+0.40i
-0.45+0.45i
-0.40+0.00i
-0.40+0.05i
-0.40+0.10i
-0.40+0.15i
-0.40+0.20i
-0.40+0.25i
-0.40+0.30i
-0.40+0.35i
-0.40+0.40i
-0.40+0.45i
-0.35+0.00i
-0.35+0.05i
-0.35+0.10i
-0.35+0.15i
-0.35+0.20i
-0.35+0.25i
-0.35+0.30i
-0.35+0.35i
-0.35+0.40i
-0.35+0.45i
-0.30+0.00i
-0.30+0.05i
-0.30+0.10i
-0.30+0.15i
-0.30+0.20i
-0.30+0.25i
-0.30+0.30i
-0.30+0.35i
-0.30+0.40i
-0.30+0.45i
-0.25+0.00i
-0.25+0.05i
-0.25+0.10i
-0.25+0.15i
-0.25+0.20i
-0.25+0.25i
-0.25+0.30i
-0.25+0.35i
-0.25+0.40i
-0.25+0.45i
-0.20+0.00i
-0.20+0.05i
-0.20+0.10i
-0.20+0.15i
-0.20+0.20i
-0.20+0.25i
-0.20+0.30i
-0.20+0.35i
-0.20+0.40i
-0.20+0.45i
-0.15+0.00i
-0.15+0.05i
-0.15+0.10i
-0.15+0.15i
-0.15+0.20i
-0.15+0.25i
-0.15+0.30i
-0.15+0.35i
-0.15+0.40i
-0.15+0.45i
-0.10+0.00i
-0.10+0.05i
-0.10+0.10i
-0.10+0.15i
-0.10+0.20i
-0.10+0.25i
-0.10+0.30i
-0.10+0.35i
-0.10+0.40i
-0.10+0.45i
0.00+0.00i
0.00+0.05i
0.00+0.10i
0.00+0.15i
0.00+0.20i
0.00+0.25i
0.00+0.30i
0.00+0.35i
0.00+0.40i
0.00+0.45i
0.05+0.00i
0.05+0.05i
0.05+0.10i
0.05+0.15i
0.05+0.20i
0.05+0.25i
0.05+0.30i
0.05+0.35i
0.05+0.40i
0.05+0.45i
0.10+0.00i
0.10+0.05i
0.10+0.10i
0.10+0.15i
0.10+0.20i
0.10+0.25i
0.10+0.30i
0.10+0.35i
0.10+0.40i
0.10+0.45i
0.15+0.00i
0.15+0.05i
0.15+0.10i
0.15+0.15i
0.15+0.20i
0.15+0.25i
0.15+0.30i
0.15+0.35i
0.15+0.40i
0.15+0.45i
0.20+0.00i
0.20+0.05i
0.20+0.10i
0.20+0.15i
0.20+0.20i
0.20+0.25i
0.20+0.30i
0.20+0.35i
0.20+0.40i
0.20+0.45i
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Eigenfunctions with Dirichlet boundary conditions (Iter. 170, Res. 200)
-0.50+0.00i: 2D
1-25
26-50
51-75
76-100
Show No.:
Go
3D
1-25
26-50
51-75
76-100
Show No.:
Go
-0.50+0.45i: 2D
1-25
26-50
51-75
76-100
Show No.:
Go
3D
1-25
26-50
51-75
76-100
Show No.:
Go
0.00+0.00i: 2D
1-25
26-50
51-75
76-100
Show No.:
Go
3D
1-25
26-50
51-75
76-100
Show No.:
Go
0.20+0.00i: 2D
1-25
26-50
51-75
76-100
Show No.:
Go
3D
1-25
26-50
51-75
76-100
Show No.:
Go
0.20+0.45i: 2D
1-25
26-50
51-75
76-100
Show No.:
Go
3D
1-25
26-50
51-75
76-100
Show No.:
Go
Eigenfunctions with Neumann boundary conditions (Iter. 170, Res. 200)
0.00+0.00i: 2D
1-25
26-50
51-75
76-100
Show No.:
Go
3D
1-25
26-50
51-75
76-100
Show No.:
Go
0.20+0.00i: 2D
1-25
26-50
51-75
76-100
Show No.:
Go
3D
1-25
26-50
51-75
76-100
Show No.:
Go
Dirichlet boundary conditions on the Basilica (c=-1.00+0.00i, Res. 30)
1000 Eigenvalues:
10 Iterations
15 Iterations
20 Iterations
25 Iterations
30 Iterations
Dirichlet boundary conditions on the Rabbit (c=-0.12+0.75i, Res. 30)
1000 Eigenvalues:
10 Iterations
15 Iterations
20 Iterations
25 Iterations
30 Iterations
Dirichlet boundary conditions on the junction point to the Basilica-bulb (c=-0.75+0.00i, Res. 30)
1000 Eigenvalues:
10 Iterations
15 Iterations
20 Iterations
25 Iterations
30 Iterations
Dirichlet boundary conditions on the junction point to the Rabbit-bulb (c=-0.12+0.70i, Res. 30)
1000 Eigenvalues:
10 Iterations
15 Iterations
20 Iterations
25 Iterations
30 Iterations
Dirichlet boundary conditions on the Basilica (c=-1.00+0.00i, Iter. 30, Res. 30)
2D:
1-25
26-50
51-75
76-100
3D:
1-25
26-50
51-75
76-100
Dirichlet boundary conditions on the Rabbit (c=-0.12+0.75i, Iter. 30, Res. 30)
2D:
1-25
26-50
51-75
76-100
3D:
1-25
26-50
51-75
76-100
Dirichlet boundary conditions on the Rabbit (c=-0.12+0.75i, Iter. 30, Res. 30)
2D:
1-25
26-50
51-75
76-100
3D:
1-25
26-50
51-75
76-100
Dirichlet boundary conditions on the junction point to the Rabbit-bulb (c=-0.12+0.70i, Iter. 30, Res. 30)
2D:
1-25
26-50
51-75
76-100
3D:
1-25
26-50
51-75
76-100
Dirichlet boundary conditions on Julia sets from the main bulb moving to the junction point to the Basilica-bulb (c=-0.75+0.00i, Iter. 30, Res. 30)
1000 Eigenvalues:
-0.70+0.00i
-0.71+0.00i
-0.72+0.00i
-0.73+0.00i
-0.74+0.00i
Dirichlet boundary conditions on Julia sets from the main bulb moving to the junction point to the Rabbit-bulb (c=-0.12+0.70i, Iter. 30, Res. 30)
Coming soon!
Dirichlet boundary conditions on quasicircles of the Basilica (c=-1.00+0.00i, Iter. 170, Res. 70): Full
1:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
2:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
3:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
4:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
Neumann boundary conditions on quasicircles of the Basilica (c=-1.00+0.00i, Iter. 170, Res. 70): Full
1:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
2:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
3:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
4:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
Dirichlet boundary conditions on quasicircles of the Rabbit (c=-0.12+0.75i, Iter. 170, Res. 70): Full
1:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
2:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
3:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
Neumann boundary conditions on quasicircles of the Rabbit (c=-0.12+0.75i, Iter. 170, Res. 70): Full
1:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
2:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
3:
1-25
26-50
51-75
76-100
Show No.:
Go
(Eigenvalues)
This page is still under construction.
Contact Information
Robert Strichartz, Cornell University, Department of Mathematics, str@math.cornell.edu
Samuel Wiese, University of Leipzig, Department of Mathematics, sw31hiqa@studserv.uni-leipzig.de