Newton's Method Gallery.

<---Real and Complex fractals
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Notes

  1. Roots: +/-1, +/-i. View Window: circle of radius 2 about 0,0
    Iterations: 128
    Coloring: Red, blue, green, and purple cosine.
    Special properties: none.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.