Roger's interests

Roger's posts

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The PC9 Breast Plate conformal map:ï»¿

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2end group based on PC9 root:

p[x_] = x^2 + 0.32968990510380686` - 0.054137451948017924` Iï»¿

p[x_] = x^2 + 0.32968990510380686` - 0.054137451948017924` Iï»¿

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My Julia renormalization at the PC4 constant:

r[z_}=Exp[I*2*Pi*GoldenRatio]

r[z_}=Exp[I*2*Pi*GoldenRatio]

**z^2**(z^2*(0.379514 +0.334932 I)+1)/(z^2+0.379514 +0.334932 I)ï»¿ Post has attachment

PC10 Julia:ï»¿

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The PC10 ISphere conformal map:ï»¿

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(* mathematica*)

Clear[x, y, a, b, c, d, w, z, c0, s]

(

p[x_] = x^2 + 0.3184722666580299` - 0.041257369922169135` I

st[i_] := {Re[z], Im[z]} /. NSolve[p[z] == 0, z][[i]]

ww = Flatten[

Table[{{a, b}, {c0, d}} /.

Solve[{x + I*y - (a*(x + I*y) + b)/(c0*(x + I*y) + d) == 0,

a + d - 2 == 0, a*d - b*c0 - 1 == 0}, {a, b, c0, d}] /.

x -> st[i][[1]] /. y -> st[i][[2]], {i, 2}], 1]

c0 = Sqrt[2]

s[i_] = ww[[i]]

{a, b} = Table[s[i], {i, 1, 2}]

{A, B} = Table[Inverse[s[i]], {i, 1, 2}] // Chopï»¿

Clear[x, y, a, b, c, d, w, z, c0, s]

(

**PC10 polynomial with 2 vertex roots**)p[x_] = x^2 + 0.3184722666580299` - 0.041257369922169135` I

st[i_] := {Re[z], Im[z]} /. NSolve[p[z] == 0, z][[i]]

ww = Flatten[

Table[{{a, b}, {c0, d}} /.

Solve[{x + I*y - (a*(x + I*y) + b)/(c0*(x + I*y) + d) == 0,

a + d - 2 == 0, a*d - b*c0 - 1 == 0}, {a, b, c0, d}] /.

x -> st[i][[1]] /. y -> st[i][[2]], {i, 2}], 1]

c0 = Sqrt[2]

s[i_] = ww[[i]]

{a, b} = Table[s[i], {i, 1, 2}]

{A, B} = Table[Inverse[s[i]], {i, 1, 2}] // Chopï»¿

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A program to solve and plot the PC_n roots:

(* mathematica*)

f[z_, c_] = z^2 + c

w[0] = {Re[c], Im[c]} /. NSolve[f[c, c] == 0, c];

w[1] = {Re[c], Im[c]} /. NSolve[f[f[c, c], c] == 0, c];

w[2] = {Re[c], Im[c]} /. NSolve[f[f[f[c, c], c], c] == 0, c];

w[3] = {Re[c], Im[c]} /. NSolve[f[f[f[f[c, c], c], c], c] == 0, c];

w[4] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[c, c], c], c], c], c] == 0, c];

w[5] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[f[c, c], c], c], c], c], c] == 0, c];

w[6] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[f[f[c, c], c], c], c], c], c], c] == 0, c];

w[7] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[f[f[f[c, c], c], c], c], c], c], c], c] == 0, c];

w[8] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[f[f[f[f[c, c], c], c], c], c], c], c], c], c] ==

0, c];

w[9] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[f[f[f[f[f[c, c], c], c], c], c], c], c], c], c],

c] == 0, c];

pts = Table[

ListPlot[w[i], PlotStyle -> {Red, PointSize[0.0075]}], {i, 0, 9}];

Show[pts, PlotRange -> {{-2, 1}, {-1.5, 1.5}}, ImageSize -> 1000]

(* end*)ï»¿

(* mathematica*)

f[z_, c_] = z^2 + c

w[0] = {Re[c], Im[c]} /. NSolve[f[c, c] == 0, c];

w[1] = {Re[c], Im[c]} /. NSolve[f[f[c, c], c] == 0, c];

w[2] = {Re[c], Im[c]} /. NSolve[f[f[f[c, c], c], c] == 0, c];

w[3] = {Re[c], Im[c]} /. NSolve[f[f[f[f[c, c], c], c], c] == 0, c];

w[4] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[c, c], c], c], c], c] == 0, c];

w[5] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[f[c, c], c], c], c], c], c] == 0, c];

w[6] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[f[f[c, c], c], c], c], c], c], c] == 0, c];

w[7] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[f[f[f[c, c], c], c], c], c], c], c], c] == 0, c];

w[8] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[f[f[f[f[c, c], c], c], c], c], c], c], c], c] ==

0, c];

w[9] = {Re[c], Im[c]} /.

NSolve[f[f[f[f[f[f[f[f[f[f[c, c], c], c], c], c], c], c], c], c],

c] == 0, c];

pts = Table[

ListPlot[w[i], PlotStyle -> {Red, PointSize[0.0075]}], {i, 0, 9}];

Show[pts, PlotRange -> {{-2, 1}, {-1.5, 1.5}}, ImageSize -> 1000]

(* end*)ï»¿

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