\( (*METODA\ DYFUZYJNA\ zastosowana\ \ do\ pewnej\ sumy\ funkcji\ Gaussa . \ \ 
Metoda\ dyfuzyjna\ polega\ na\ odksztalceniu\ funkcji\ V -> Vt\ takim, \ 
      ze\ Vt\ 
ma\ juz\ tylko\ jedno\ minimum, \ 
      ktore\ z\ latwoscia\ znajdujemy . \ 
            Potem\ nastepuje\ sekwencja\ par\ \(operacji : \ 
zmniejszenie\ odksztalcenia\ i\ minimalizacja\ az\ do\ uzyskania\ ksztaltu\ Vt\) = 
        V . \ Wtedy\ 
"powinnismy byc"\ w\ minimum\ globalnym . \ 
            I\ w\ tym\ przypadku\ \(\(jestesmy\)\(.\)\)\ *) 
V = \(-2\)\ E\^\(\(-0.1\)\ \((x - 3)\)\^2 - 0.2\ y\^2\) - 
        3\ E\^\(\(-0.5\)\ \((x - 5)\)\^2 - 0.4\ \((y + 4)\)\^2\) - 
        7\ E\^\(\(-0.1\)\ \((x + 5)\)\^2 - 0.5\ \((y - 5)\)\^2\) - 
        2\ E\^\(\(-0.2\)\ \((x + 5)\)\^2 - 0.2\ \((y + 5)\)\^2\)\)
Plot3D[V, {x, -8, 8}, {y, -8, 8}, 
      PlotPoints -> 30] 
ContourPlot[V, {x, -9, 9}, {y, -9, 9}, 
      PlotPoints -> 20]
t = 20
Vt = -((2 (E^(-((0.1 (((x - 3))^2))/(1 + 4 0.1 t)) - ((0.2 (y^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.2 t)])) - ((3 (E^(-((0.5 (((x - 5))^2))/(1 + 4 0.5 t)) - ((0.4 (((y + 4))^2))/(1 + 4 0.4 t)))))/(Sqrt[(1 + 4 0.5 t) (1 + 4 0.4 t)])) - ((7 (E^(-((0.1 (((x + 5))^2))/(1 + 4 0.1 t)) - ((0.5 (((y - 5))^2))/(1 + 4 0.5 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.5 t)])) - ((2 (E^(-((0.2 (((x + 5))^2))/(1 + 4 0.2 t)) - ((0.2 (((y + 5))^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.2 t) (1 + 4 0.2 t)]))
Plot3D[Vt, {x, -8, 8}, {y, -8, 8}, 
      PlotPoints -> 30]
ContourPlot[Vt, {x, -9, 9}, {y, -9, 9}]
t = 10
Vt = -((2 (E^(-((0.1 (((x - 3))^2))/(1 + 4 0.1 t)) - ((0.2 (y^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.2 t)])) - ((3 (E^(-((0.5 (((x - 5))^2))/(1 + 4 0.5 t)) - ((0.4 (((y + 4))^2))/(1 + 4 0.4 t)))))/(Sqrt[(1 + 4 0.5 t) (1 + 4 0.4 t)])) - ((7 (E^(-((0.1 (((x + 5))^2))/(1 + 4 0.1 t)) - ((0.5 (((y - 5))^2))/(1 + 4 0.5 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.5 t)])) - ((2 (E^(-((0.2 (((x + 5))^2))/(1 + 4 0.2 t)) - ((0.2 (((y + 5))^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.2 t) (1 + 4 0.2 t)]))
Plot3D[Vt, {x, -8, 8}, {y, -8, 8}, 
      PlotPoints -> 30]
ContourPlot[Vt, {x, -9, 9}, {y, -9, 9}]
t = 5
Vt = -((2 (E^(-((0.1 (((x - 3))^2))/(1 + 4 0.1 t)) - ((0.2 (y^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.2 t)])) - ((3 (E^(-((0.5 (((x - 5))^2))/(1 + 4 0.5 t)) - ((0.4 (((y + 4))^2))/(1 + 4 0.4 t)))))/(Sqrt[(1 + 4 0.5 t) (1 + 4 0.4 t)])) - ((7 (E^(-((0.1 (((x + 5))^2))/(1 + 4 0.1 t)) - ((0.5 (((y - 5))^2))/(1 + 4 0.5 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.5 t)])) - ((2 (E^(-((0.2 (((x + 5))^2))/(1 + 4 0.2 t)) - ((0.2 (((y + 5))^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.2 t) (1 + 4 0.2 t)]))
Plot3D[Vt, {x, -8, 8}, {y, -8, 8}, 
      PlotPoints -> 30]
ContourPlot[Vt, {x, -9, 9}, {y, -9, 9}, 
      PlotPoints -> 20]
t = 2
Vt = -((2 (E^(-((0.1 (((x - 3))^2))/(1 + 4 0.1 t)) - ((0.2 (y^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.2 t)])) - ((3 (E^(-((0.5 (((x - 5))^2))/(1 + 4 0.5 t)) - ((0.4 (((y + 4))^2))/(1 + 4 0.4 t)))))/(Sqrt[(1 + 4 0.5 t) (1 + 4 0.4 t)])) - ((7 (E^(-((0.1 (((x + 5))^2))/(1 + 4 0.1 t)) - ((0.5 (((y - 5))^2))/(1 + 4 0.5 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.5 t)])) - ((2 (E^(-((0.2 (((x + 5))^2))/(1 + 4 0.2 t)) - ((0.2 (((y + 5))^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.2 t) (1 + 4 0.2 t)]))
Plot3D[Vt, {x, -8, 8}, {y, -8, 8}, 
      PlotPoints -> 30]
ContourPlot[Vt, {x, -9, 9}, {y, -9, 9}, 
      PlotPoints -> 20]
t = 1
Vt = -((2 (E^(-((0.1 (((x - 3))^2))/(1 + 4 0.1 t)) - ((0.2 (y^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.2 t)])) - ((3 (E^(-((0.5 (((x - 5))^2))/(1 + 4 0.5 t)) - ((0.4 (((y + 4))^2))/(1 + 4 0.4 t)))))/(Sqrt[(1 + 4 0.5 t) (1 + 4 0.4 t)])) - ((7 (E^(-((0.1 (((x + 5))^2))/(1 + 4 0.1 t)) - ((0.5 (((y - 5))^2))/(1 + 4 0.5 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.5 t)])) - ((2 (E^(-((0.2 (((x + 5))^2))/(1 + 4 0.2 t)) - ((0.2 (((y + 5))^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.2 t) (1 + 4 0.2 t)]))
Plot3D[Vt, {x, -8, 8}, {y, -8, 8}, 
      PlotPoints -> 30]
ContourPlot[Vt, {x, -9, 9}, {y, -9, 9}, 
      PlotPoints -> 20]
t = 0
Vt = -((2 (E^(-((0.1 (((x - 3))^2))/(1 + 4 0.1 t)) - ((0.2 (y^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.2 t)])) - ((3 (E^(-((0.5 (((x - 5))^2))/(1 + 4 0.5 t)) - ((0.4 (((y + 4))^2))/(1 + 4 0.4 t)))))/(Sqrt[(1 + 4 0.5 t) (1 + 4 0.4 t)])) - ((7 (E^(-((0.1 (((x + 5))^2))/(1 + 4 0.1 t)) - ((0.5 (((y - 5))^2))/(1 + 4 0.5 t)))))/(Sqrt[(1 + 4 0.1 t) (1 + 4 0.5 t)])) - ((2 (E^(-((0.2 (((x + 5))^2))/(1 + 4 0.2 t)) - ((0.2 (((y + 5))^2))/(1 + 4 0.2 t)))))/(Sqrt[(1 + 4 0.2 t) (1 + 4 0.2 t)]))
Plot3D[Vt, {x, -8, 8}, {y, -8, 8}, 
      PlotPoints -> 30]
ContourPlot[Vt, {x, -9, 9}, {y, -9, 9}, 
      PlotPoints -> 20]