• New dual carton method for Besicovitch-Ursell-Knopp->Mandelbrot cartoon

    From Roger Bagula@21:1/5 to All on Tue Mar 26 11:47:53 2019
    This method is the one dimensional Mandelbrot cartoon method of his many papers made into 2 dimensional and 3 dimensional versions. Dr. Edgar calls the Besicovith-Ursell -Knopp , I call them biscuits. They are generated by cartoons. I just discovered
    that you can use dual 2 dimensional cartoon from Root structures or traditional cartoons to make nice new fractals. You define the similarity dimension in the fractal and the result is a self -similar fractal. The ratios are usually larger : Sierpinski
    gasket IFS ratio=2: In biscuits ratio =3. Read Mandelbrot's papers on cartoon methods.
    (* mathematica*)
    Clear[f, g, h, k]
    (* Minkowski sausage cartoon*)
    r = {{1/2, 0}, {1/2, 1/4}, {0,
    1/4}, {0, 1/2}, {1, 1/2}, {1, 3/4}, {1/2, 3/4}, {1/2, 1}}
    ListLinePlot[r]
    f[x_] := r[[1, 1]] /; 0 <= x <= 1/8
    f[x_] := r[[2, 1]] /; 1/8 < x <= 2/8
    f[x_] := r[[3, 1]] /; 2/8 < x <= 3/8
    f[x_] := r[[4, 1]] /; 3/8 < x <= 4/8
    f[x_] := r[[5, 1]] /; 4/8 < x <= 5/8
    f[x_] := r[[6, 1]] /; 5/8 < x <= 6/8
    f[x_] := r[[7, 1]] /; 6/8 < x <= 7/8
    f[x_] := r[[8, 1]] /; 7/8 < x <= 1
    ff[x_] = f[Mod[Abs[x], 1]]
    f[Mod[Abs[x], 1]]
    Plot[ff[x], {x, 0, 4}]
    g[x_] := r[[1, 2]] /; 0 <= x <= 1/8
    g[x_] := r[[2, 2]] /; 1/8 < x <= 2/8
    g[x_] := r[[3, 2]] /; 2/8 < x <= 3/8
    g[x_] := r[[4, 2]] /; 3/8 < x <= 4/8
    g[x_] := r[[5, 2]] /; 4/8 < x <= 5/8
    g[x_] := r[[6, 2]] /; 5/8 < x <= 6/8
    g[x_] := r[[7, 2]] /; 6/8 < x <= 7/8
    g[x_] := r[[8, 2]] /; 7/8 < x <= 1
    gg[x_] = g[Mod[Abs[x], 1]]
    g[Mod[Abs[x], 1]]
    Plot[gg[x], {x, 0, 4}]
    ParametricPlot[{ff[x], gg[x]}, {x, 0, 1}, PlotStyle -> Red]
    s0 = N[0.5]
    0.5`
    kk[x_] = Sum[ff[3^k*x]/3^(s0*k), {k, 0, 20}];
    Plot[kk[x], {x, 0, 4}]
    ll[x_] = Sum[gg[3^k*(x)]/3^(s0*k), {k, 0, 20}];
    Plot[ll[x], {x, 0, 4}]
    jj[x_] = Sum[ff[3^k*(x - 1/2)]/3^(s0*k), {k, 0, 20}];
    Plot[jj[x], {x, 0, 4}]
    ParametricPlot[{kk[t], ll[t]}, {t, 0, 1}]
    aa = Table[{ll[n/100000], kk[n/100000]}, {n, 0, 100000}];
    ListPlot[aa, PlotStyle -> {PointSize[0.001], Red}, ImageSize -> 1000]
    cc = Table[{jj[n/100000], kk[n/100000]}, {n, 0, 100000}];
    ListPlot[cc, PlotStyle -> {PointSize[0.001], Red}, ImageSize -> 1000]
    b = Table[{ll[n/100000], kk[n/100000], jj[n/100000]}, {n, 0,
    100000}];
    g1 = ListPointPlot3D[b, PlotStyle -> {PointSize[0.001]},
    ImageSize -> 1000, ColorFunction -> "Rainbow", Background -> Black,
    ViewPoint -> {1, 1, 1}*5];
    g2 = Show[g1, ViewPoint -> Top];
    g3 = Show[g1, ViewPoint -> Front]; Export["8step_Minkowski_Sausage_xydualcartoon3d3scale.jpg", {g1, g2,
    g3}]
    (*end*) https://scontent-lax3-2.xx.fbcdn.net/v/t1.0-9/55646619_10157162494421499_355221377659174912_o.jpg?_nc_cat=106&_nc_oc=AQlxjNEGKzLoeEamNCiccjOhmLlvhWoglYN8sFbtLdptm_parDs-d6l9M51k3TSFdL4&_nc_ht=scontent-lax3-2.xx&oh=769aff16b329c16289b1e9b64d0298ef&oe=
    5D45184A

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  • From Roger Bagula@21:1/5 to All on Tue Mar 26 11:51:46 2019
    Posted 6 years ago: https://plus.google.com/11080389016834319…/posts/VGUqktztpvR
    ( going away soon)

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  • From Roger Bagula@21:1/5 to All on Tue Mar 26 11:53:44 2019
  • From Roger Bagula@21:1/5 to All on Tue Mar 26 12:01:33 2019
    https://www.semanticscholar.org/paper/Scaling-in-financial-prices-%3A-III-.-Cartoon-motions-Mandelbrot/807646b49446b9da5c43305cbe7de22451003549
    Figure 5. Stack of shuffled multifractal cartoons with y = 2/3 therefore H = 1/2 and—from the top down—the following values of x : 0.2222, 0.3333, 0.3889, 0.4444 (Fickian, starred), 0.4556, 0.4667, 0.4778, and 0.4889. Unconventional but true, all the
    increments plotted in the right column are spectrally white. However, only one line in that column is near-Brownian; it is the starred Fickian line for x = 4/9.
    https://www.semanticscholar.org/paper/Scaling-in-financial-prices-%3A-III-.-Cartoon-motions-Mandelbrot/807646b49446b9da5c43305cbe7de22451003549/figure/4

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  • From Roger Bagula@21:1/5 to All on Tue Mar 26 12:10:08 2019
    The climate change -global warming world war projected:
    Here I suppose that ancient greed is modern greed and wars continue in the ancient vain of territory gain.
    I added 11 modern wars with territory gain estimated and one ancient war (fall of ancient Persian Empire):
    https://en.wikipedia.org/wiki/Greco-Persian_Wars
    and then, I added a World War III as a Turchen-Climate war in 2026.
    This model is set in 7 cycles of 7 Kondratieff -Jubilee cycles and
    gives a 51 year long cycle. Why 2026? I did a weather/rainfall projection
    and 2026 is when the global warming dry cycle ends ( with massive hurricanes world wide
    caused by temperature rise, ice melting and human produced CO2).

    Solve[N[(2026 + 500)/x] - 49 == 0, x]
    {{x -> 51.551}}
    N[(2026 + 500)/(7*51.55102040816327)]
    7.

    The fall of the modern civilization in a prolonged world war over the climate changing world’s limited resources.

    (Mathematica)
    (* page154:Raoul Naroll: Deterrence in History:Theory and \
    Research on the Causes of War, Dean G. Pruit and Richard C. Snyder*)
    (* {x,y,z}={year, duration months,gain of territory}: 11 modern wars and \ projected Turchin-Global Warming world war *)
    w = {{-499, 50*12, 100}, {-225,
    49, 34}, {-25, 37, 57}, {176, 49, 49}, {376, 55, 40}, {576, 66, 61}, {1276,
    37, 40}, {1576, 66, 38}, {1676, 51, 60}, {1776, 55, 34}, {1376, 45,
    61}, {1476, 44, 58}, {1576, 37, 49}, {1476, 42, 63}, {776, 56, 50}, {-125,
    66, 59}, {-25, 37, 50}, {776, 52, 49}, {1076, 49, 49}, {1376, 39,
    60}, {1803, 9*12, 60}, {1860, 4*12, 50}, {1912, 7*12, 100}, {1937, 6*12,
    100}, {1953, 4*12, 50}, {1964, 9*12, 50}, {1979, 10*12, 50}, {1990, 5,
    25}, {2003, 8*12, 25}, {2014, 3*12, 50}, {2001, 17*12, 50}, {2026, 6*12,
    100}}
    s = Sum[w[[i, 3]], {i, Length[w]}]
    ListPointPlot3D[w, ColorFunction -> "Rainbow", Background -> Black,
    ImageSize -> 1000]
    (* Function as Gaussian events with sigma as the scaled duration of conflict \ and magnitude as territorial gain*)

    f[x_] = Sum[
    w[[i, 3]]Exp[-(x - w[[i, 1]])^2/(2(w[[i, 2]]/(5.5*12))^2)], {i,
    Length[w]}];
    g1 = Plot[f[x], {x, -500, 2040}, PlotRange -> All, ImageSize -> 1000,
    PlotStyle -> Red]
    g[x_] = D[f[x], {x, 1}];
    g2 = Plot[g[x], {x, -500, 2040}, PlotRange -> All, ImageSize -> 1000,
    PlotStyle -> Green]
    h[x_] = D[f[x], {x, 2}];
    g3 = Plot[h[x], {x, -500, 2040}, PlotRange -> All, ImageSize -> 1000,
    PlotStyle -> Cyan]
    (* linearized polynomial fit to the Gaussian distribution*)

    t = Table[f[x], {x, -500, 2040, 1/20}];
    j[x_] = Fit[t, Table[x^i, {i, Length[w]}], x]
    (* scaled to the output graph*)
    g4 =
    Plot[5*j[20*x + 500*20], {x, -500, 2100},
    PlotRange -> {{-500, 2100}, {-50, 150}}, ImageSize -> 1000,
    PlotStyle -> Black]
    Show[{g1, g2, g4}]
    a = NIntegrate[f[x], {x, -500, 2020}]
    s/a
    b = Integrate[12*j[20*x + 500*20], {x, -500, 2020}]
    b/a
    (end)

    Doom and Gloom isn't real popular, but people really need to know the way the arrow is pointing!
    I've been studying historical cycles since the late 70's. The 7 long cycles/50 year cycles that goes with the rise and fall of civilizations is called the "year of years" cycle even though it is shorter than 365 years. The causation of the cycles in
    ancient times was mostly climate cycles that depended on solar intensity ( sun spot cycle), which I found has a certain Cantor like dimensional dependence. The current crisis is really a multiplied climate cycle magnified by human CO2 production that
    traps heat in the atmosphere. That the world situation will come to a world war is just a best guess that the calculation seems to support. China against the USA and Europe would be the best bet....

    This is one time I really hope I’m wrong.

    https://plus.google.com/photos/110803890168343196795/album/6613033002651352673/6613033002852651762?authkey=CLPtxJys94Whfw&sqid=105666856644891680204&ssid=ff5a5216-4bca-4da5-a044-148e83b553d4

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  • From Roger Bagula@21:1/5 to All on Wed Mar 27 12:33:58 2019
    I found a paper online:used in financial analysis: http://mail.ipb.ac.rs/~vrhovac/sloba/bib/1-s2.0-S0378437114003811-main.pdf

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