Newton's Method Gallery.
<---Real and Complex fractals
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Notes
- Roots: +/-1, +/-i.
View Window: circle of radius 2 about 0,0
Iterations: 128
Coloring: Red, blue, green, and purple cosine.
Special properties: none.
- Roots: +/-1, 0.5+/-0.866i, -0.5+/-0.866i.
View Window: circle of radius 2 about 0,0
Iterations: 128
Coloring: Red, blue, green, purple, cyan, and gold cosine.
Special properties: none.
- Roots: -1.5-1.2i, -1.8i, 1.5-1.2i,
-1.5+1.2i, 1.8i, 1.5+1.2i
View Window Corners: (-4,-4), (4,4)
Iterations: 128
Coloring: Red, blue, green, purple, cyan, and gold cosine.
Special properties: none.
- Roots: -2+i,-1+2i,2-i,1-2i
View Window Corners: (-1.6,1.6), (1.6,1.6)
Iterations: 128
Coloring: Red, blue, green, and gold cosine.
Special properties: none.
- Roots: -1.5-1.2i, -1.8i, 1.5-1.2i,
-1.5+1.2i, 1.8i, 1.5+1.2i
View Window Corners: (0.59,-1.39), (0.97,-1.01)
Iterations: 128
Coloring: Red, blue, green, purple, cyan, and gold cosine.
Special properties: none.
- Roots: -1.5-1.2i, -1.8i, 1.5-1.2i,
-1.5+1.2i, 1.8i, 1.5+1.2i
View Window Corners: (0.59,-1.39), (0.97,-1.01)
Iterations: 128
Coloring: gold cosine.
Special properties: All roots except fifth mapped to deep purple.
- Roots:2.26588+2.90939i, -1.50633-1.86378i,
0.33489-0.530382i, -2.57296-2.12984i,
-2.26588+2.90939i, 1.50633-1.86378i,
-0.33489-0.530382i, 2.57296-2.12984i, 0.029466i,
0.869046i, -2.70772i, 3.89937i,
0+3.46099i
View Window Corners: (-0.4,-2), (0.4,1.2)
Iterations: 128
Coloring: Cosine as shown.
Special properties: none.
- Roots:-3.93561-3.27027i, 1.93905-3.51878i,
-0.232187+1.83607i, -2.79398+3.71021i,
3.93561-3.27027i, -1.93905-3.51878i,
0.232187+1.83607i, 2.79398+3.71021i,2.10593i,
-1.31438i,+0.740117i, -1.35776i,
-1.33735i
View Window Corners: (-0.4,-2), (0.4,1.2)
Iterations: 128
Coloring: Cosine as shown.
Special properties: none.
- Roots: -0.0699356+3.27662i, 1.56931+3.37789i,
-0.610239+0.74703i, -2.94133-0.396418i,
0.0699356+3.27662i, -1.56931+3.37789i,
0.610239+0.74703i, 2.94133-0.396418i, -1.84309i,
+2.56333i, -2.29466i, -2.33002i, +3.46376i
View Window Corners: (-0.4,-2), (0.4,1.2)
Iterations: 128
Coloring: Cosine as shown.
Special properties: none.
- Roots:0i,1.4-0.9i,-1.4-0.9i,1.1+2.23i,
-1.1+2.23i,-4.8i,+3.35i
View Window Corners: (-0.7,1.69), (0.7,1.3.09)
Iterations: 96
Coloring: Cosine, first root is dark purple and others are white.
Special properties: none.
- Roots:0i,1.4-0.9i,-1.4-0.9i,1.1+2.23i,
-1.1+2.23i,-4.8i,+3.35i
View Window Corners: (-0.7,1.69), (0.7,1.3.09)
Iterations: 96
Coloring: Cosine, first root is foil colored while the rest are
dark purple.
Special properties: foil coloring a cosine coloring where the
color depends on the number of iterations to convergence.
- Roots:-1.99153-2.32841i, 3.52742-0.619636i,
-0.832855-0.939483i, 1.99153-2.32841i,
-3.52742-0.619636i, 0.832855-0.939483i,
-2.14616i, +0.284378i, +0.265678i
View Window Corners: (-2.5,-4),(2.5,1)
Iterations: 96
Coloring: Cosine, as shown.
Special properties: striping results from very nearby roots.
- Roots:1+2i,2+1i,-1-2i,-2-1i
View Window Corners: (-2,-2),(2,2)
Iterations: 7
Coloring: Cosine, red, green, blue, yellow, with cyan for
non-convergence.
Special properties: convergence is to roots plus
0.022+0.022i, this causes the blobby coloring.
- Roots:1+2i,2+1i,-1-2i,-2-1i
View Window Corners: (0,-1),(1,0)
Iterations: 96
Coloring: Cosine, red, green, blue, yellow.
Special properties: none.
- Roots:0, 1+2i, 2+1i, -1-2i, -2-1i
View Window Corners: (-2,-2),(0,0)
Iterations: 96
Coloring: Cosine, red, green, blue, yellow, violet.
Special properties: none.
- Roots:3.94131+0.945035i, -0.657448-1.1713i,
-1.02188+2.516i, -2.21983+2.23106i,
-1.70883-3.15755i, 2.18153+2.03722i,
0.288389-1.89953i, -3.94131+0.945035i,
0.657448-1.1713i, 1.02188+2.516i,
2.21983+2.23106i, 1.70883-3.15755i,
-2.18153+2.03722i, -0.288389-1.89953i, -2.69272i,
-2.34123i, -1.71451i
View Window Corners: (-2.1,1.6),(-0.6,3.1)
Iterations: 128
Coloring: Cosine, white-to-gold by iteration number.
Special properties: none.
- Roots:-0.707835-2.98367i, 1.04032+0.213649i,
-3.73542+0.608763i, -1.51357+2.95287i,
2.81457-3.21074i, 3.96002-2.08961i,
1.94319-0.451486i, 0.707835-2.98367i,
-1.04032+0.213649i, 3.73542+0.608763i,
1.51357+2.95287i, -2.81457-3.21074i,
-3.96002-2.08961i, -1.94319-0.451486i, -1.10175i,
+2.46269i, +1.83443i
View Window Corners: (-0.9,0.5),(0.9,2.3)
Iterations: 128
Coloring: Cosine, white-to-blue by iteration number.
Special properties: none.
- Roots:-0.707835-2.98367i, 1.04032+0.213649i,
-3.73542+0.608763i, -1.51357+2.95287i,
2.81457-3.21074i, 3.96002-2.08961i,
1.94319-0.451486i, 0.707835-2.98367i,
-1.04032+0.213649i, 3.73542+0.608763i,
1.51357+2.95287i, -2.81457-3.21074i,
-3.96002-2.08961i, -1.94319-0.451486i, -1.10175i,
+2.46269i, +1.83443i
View Window Corners: (-0.45,2.18),(0.45,2.27)
Iterations: 128
Coloring: Cosine, as shown.
Special properties: none.