PhaseDiagram.sagews

#######################
#Phase Diagram
#by Sinan Kapcak
#2017
#www.k-interact.net/dds
#######################

a,b,c,d, x,y=var('a b c d x y')
@interact
def _(parameters=selector(['0','1', '2','3','4'],label='Number of parameters in the system',buttons=False,default='0'),
      intx=input_box(label='Slider interval for $x_0$',default=(0,10 ),width=20 ),
      inty=input_box(label='Slider interval for $y_0$',default=(0,10 ),width=20 )
     ):
    if parameters=='0':
        @interact#(layout=dict(bottom=[['x0'],['y0'],['iterasyon'],['figs']],top=[['f'],['g'],['segment_check'],['isoclines_check']]))
        def _(
            f=input_box(label='$f(x,y)$',default=x-n(.6,digits=2)  *sin(y),width=40),
            g=input_box(label='$g(x,y)$',default=cos(x),width=40),
            x0=slider(intx[0], intx[1], .05, default=(intx[0]+intx[1])/2,label='$x_0$'),y0=slider(inty[0],inty[1], .05, default=(inty[0]+inty[1])/2  ,label='$y_0$'),
            iterasyon=input_box(default=100,label='Number of iterations',width=12),
            segment_check = ("Joined Points", True),
            isoclines_check = ("Show Isoclines", False),
            figs=slider(2, 20, 1, default=5,label='Figure size'),
            ar=slider([2^s for s in [-10..10]], default=1,label='Aspect Ratio' )
):
            nok=[(x0,y0)]#list of points
            for i in range(iterasyon):
                nok.append((f(x=nok[i][0],y=nok[i][1]),g(x=nok[i][0],y=nok[i][1])))
                graf_nok=point(nok,frame=False,rgbcolor='black', pointsize=10,figsize=figs,aspect_ratio=ar)#, legend_label='origin')
                graf_ilk=point(nok[0],rgbcolor='green', pointsize=40)
                graf_son=point(nok[-1],rgbcolor='red', pointsize=40)
                graf_segments=list_plot(nok, plotjoined=True, color='purple',alpha=.3)
                graf=graf_ilk+graf_son+graf_nok
                if segment_check:
                    graf = graf + graf_segments
                if isoclines_check:
                    nok_x= [nok[i][0] for i in range(len(nok)) ]
                    mi_x=min(nok_x)
                    ma_x=max(nok_x)
                    nok_y= [nok[i][1] for i in range(len(nok)) ]
                    mi_y=min(nok_y)
                    ma_y=max(nok_y)
                    fark_x=ma_x-mi_x
                    fark_y=ma_y-mi_y
                    mi1_x=1.1*mi_x-.1*ma_x
                    ma1_x=1.1*ma_x-.1*mi_x
                    mi1_y=1.1*mi_y-.1*ma_y
                    ma1_y=1.1*ma_y-.1*mi_y
                    isocline1=implicit_plot(x==f, (x,mi1_x,ma1_x), (y,mi1_y,ma1_y),legend_label='iso1',rgbcolor='orange')
                    isocline2=implicit_plot(y==g, (x,mi1_x,ma1_x), (y,mi1_y,ma1_y),legend_label='iso2',rgbcolor='brown')
                    graf = graf + isocline1 + isocline2
            show(graf,frame=True,axes=False,axes_labels=['$x_n$','$y_n$'])
    if parameters=='1':
        @interact
        def _(paramint1=input_box(label='Slider interval for paramater $a$',default=(0,10),width=20)):
            @interact(layout=dict(bottom=[['param1'],['x0'],['y0'],['iterasyon'],['figs']],top=[['f'],['g'],['segment_check'],['isoclines_check']]))
            def _(
                param1=slider(paramint1[0], paramint1[1], .05, default=(paramint1[0]+ paramint1[1])/2,label='$a$'),
                f=input_box(label='$f(x,y)$',default=x-(a-1)*sin(y/a),width=40),
                g=input_box(label='$g(x,y)$',default=a*cos(x/a),width=40),
                x0=slider(intx[0], intx[1], .05, default=(intx[0]+intx[1])/2,label='$x_0$'),y0=slider(inty[0],inty[1], .05, default=(inty[0]+inty[1])/2  ,label='$y_0$'),
                iterasyon=input_box(default=100,label='Number of iterations',width=12),
                segment_check = ("Joined Points", True),
                isoclines_check = ("Show Isoclines", False),figs=slider(2, 20, 1, default=5,label='Figure size'),
                ar=slider([2^s for s in [-10..10]], default=1,label='Aspect Ratio' )
            ):
                f=f(a=param1)
                g=g(a=param1)
                nok=[(x0,y0)]#list of points
                for i in range(iterasyon):
                    nok.append((f(x=nok[i][0],y=nok[i][1],a=param1),g(x=nok[i][0],y=nok[i][1],a=param1)))
                    graf_nok=point(nok,frame=False,rgbcolor='black', pointsize=10,figsize=figs,aspect_ratio=ar)#, legend_label='origin')
                    graf_ilk=point(nok[0],rgbcolor='green', pointsize=40)
                    graf_son=point(nok[-1],rgbcolor='red', pointsize=40)
                    graf_segments=list_plot(nok, plotjoined=True, color='purple',alpha=.3)
                    graf=graf_ilk+graf_son+graf_nok
                    if segment_check:
                        graf = graf + graf_segments
                    if isoclines_check:
                        nok_x= [nok[i][0] for i in range(len(nok)) ]
                        mi_x=min(nok_x)
                        ma_x=max(nok_x)
                        nok_y= [nok[i][1] for i in range(len(nok)) ]
                        mi_y=min(nok_y)
                        ma_y=max(nok_y)
                        fark_x=ma_x-mi_x
                        fark_y=ma_y-mi_y
                        mi1_x=1.1*mi_x-.1*ma_x
                        ma1_x=1.1*ma_x-.1*mi_x
                        mi1_y=1.1*mi_y-.1*ma_y
                        ma1_y=1.1*ma_y-.1*mi_y
                        isocline1=implicit_plot(x==f, (x,mi1_x,ma1_x), (y,mi1_y,ma1_y),legend_label='iso1',rgbcolor='orange')
                        isocline2=implicit_plot(y==g, (x,mi1_x,ma1_x), (y,mi1_y,ma1_y),legend_label='iso2',rgbcolor='brown')
                        graf = graf + isocline1 + isocline2
                show(graf,frame=True,axes=False,axes_labels=['$x_n$','$y_n$'])
    if parameters=='2':
        @interact
        def _(paramint1=input_box(label='Slider interval for paramater $a$',default=(0,4),width=20),
             paramint2=input_box(label='Slider interval for paramater $b$',default=(0,4),width=20)):
            @interact#(layout=dict(bottom=[['param1'],['x0'],['y0'],['iterasyon'],['figs']],top=[['f'],['g'],['segment_check'],['isoclines_check']]))
            def _(
                param1=slider(paramint1[0], paramint1[1], .05, default=(paramint1[0]+ paramint1[1])/2,label='$a$'),
                param2=slider(paramint2[0], paramint2[1], .05, default=(paramint2[0]+ paramint2[1])/2,label='$b$'),
                f=input_box(label='$f(x,y)$',default=x*exp(a*(1-x)-y),width=40),
                g=input_box(label='$g(x,y)$',default=b*x*(1-exp(-y)),width=40),
                x0=slider(intx[0], intx[1], .05, default=(intx[0]+intx[1])/2,label='$x_0$'),y0=slider(inty[0],inty[1], .05, default=(inty[0]+inty[1])/2  ,label='$y_0$'),
                iterasyon=input_box(default=100,label='Number of iterations',width=12),
                segment_check = ("Joined Points", True),
                isoclines_check = ("Show Isoclines", False),figs=slider(2, 20, 1, default=5,label='Figure size'),
                ar=slider([2^s for s in [-10..10]], default=1,label='Aspect Ratio' )
            ):
                f=f(a=param1,b=param2)
                g=g(a=param1,b=param2)
                nok=[(x0,y0)]#list of points
                for i in range(iterasyon):
                    nok.append((f(x=nok[i][0],y=nok[i][1],a=param1,b=param2),g(x=nok[i][0],y=nok[i][1],a=param1,b=param2)))
                    graf_nok=point(nok,frame=False,rgbcolor='black', pointsize=10,figsize=figs,aspect_ratio=ar)#, legend_label='origin')
                    graf_ilk=point(nok[0],rgbcolor='green', pointsize=40)
                    graf_son=point(nok[-1],rgbcolor='red', pointsize=40)
                    graf_segments=list_plot(nok, plotjoined=True, color='purple',alpha=.3)
                    graf=graf_ilk+graf_son+graf_nok
                    if segment_check:
                        graf = graf + graf_segments
                    if isoclines_check:
                        nok_x= [nok[i][0] for i in range(len(nok)) ]
                        mi_x=min(nok_x)
                        ma_x=max(nok_x)
                        nok_y= [nok[i][1] for i in range(len(nok)) ]
                        mi_y=min(nok_y)
                        ma_y=max(nok_y)
                        fark_x=ma_x-mi_x
                        fark_y=ma_y-mi_y
                        mi1_x=1.1*mi_x-.1*ma_x
                        ma1_x=1.1*ma_x-.1*mi_x
                        mi1_y=1.1*mi_y-.1*ma_y
                        ma1_y=1.1*ma_y-.1*mi_y
                        isocline1=implicit_plot(x==f, (x,mi1_x,ma1_x), (y,mi1_y,ma1_y),legend_label='iso1',rgbcolor='orange')
                        isocline2=implicit_plot(y==g, (x,mi1_x,ma1_x), (y,mi1_y,ma1_y),legend_label='iso2',rgbcolor='brown')
                        graf = graf + isocline1 + isocline2
                show(graf,frame=True,axes=False,axes_labels=['$x_n$','$y_n$'])
    if parameters=='3':
        @interact
        def _(paramint1=input_box(label='Slider interval for paramater $a$',default=(0,10),width=20),
             paramint2=input_box(label='Slider interval for paramater $b$',default=(0,10),width=20),
             paramint3=input_box(label='Slider interval for paramater $c$',default=(0,10),width=20)):
            @interact#(layout=dict(bottom=[['param1'],['x0'],['y0'],['iterasyon'],['figs']],top=[['f'],['g'],['segment_check'],['isoclines_check']]))
            def _(
                param1=slider(paramint1[0], paramint1[1], .05, default=(paramint1[0]+ paramint1[1])/2,label='$a$'),
                param2=slider(paramint2[0], paramint2[1], .05, default=(paramint2[0]+ paramint2[1])/2,label='$b$'),
                param3=slider(paramint3[0], paramint3[1], .05, default=(paramint3[0]+ paramint3[1])/2,label='$c$'),
                f=input_box(label='$f(x,y)$',default=x+(1-a)*sin(y/b),width=40),
                g=input_box(label='$g(x,y)$',default=c*cos(x/a),width=40),
                x0=slider(intx[0], intx[1], .05, default=(intx[0]+intx[1])/2,label='$x_0$'),y0=slider(inty[0],inty[1], .05, default=(inty[0]+inty[1])/2  ,label='$y_0$'),
                iterasyon=input_box(default=100,label='Number of iterations',width=12),
                segment_check = ("Joined Points", True),
                isoclines_check = ("Show Isoclines", False),figs=slider(2, 20, 1, default=5,label='Figure size'),
                ar=slider([2^s for s in [-10..10]], default=1,label='Aspect Ratio' )
            ):
                f=f(a=param1,b=param2,c=param3)
                g=g(a=param1,b=param2,c=param3)
                nok=[(x0,y0)]#list of points
                for i in range(iterasyon):
                    nok.append((f(x=nok[i][0],y=nok[i][1],a=param1,b=param2,c=param3),g(x=nok[i][0],y=nok[i][1],a=param1,b=param2,c=param3)))
                    graf_nok=point(nok,frame=False,rgbcolor='black', pointsize=10,figsize=figs,aspect_ratio=ar)#, legend_label='origin')
                    graf_ilk=point(nok[0],rgbcolor='green', pointsize=40)
                    graf_son=point(nok[-1],rgbcolor='red', pointsize=40)
                    graf_segments=list_plot(nok, plotjoined=True, color='purple',alpha=.3)
                    graf=graf_ilk+graf_son+graf_nok
                    if segment_check:
                        graf = graf + graf_segments
                    if isoclines_check:
                        nok_x= [nok[i][0] for i in range(len(nok)) ]
                        mi_x=min(nok_x)
                        ma_x=max(nok_x)
                        nok_y= [nok[i][1] for i in range(len(nok)) ]
                        mi_y=min(nok_y)
                        ma_y=max(nok_y)
                        fark_x=ma_x-mi_x
                        fark_y=ma_y-mi_y
                        mi1_x=1.1*mi_x-.1*ma_x
                        ma1_x=1.1*ma_x-.1*mi_x
                        mi1_y=1.1*mi_y-.1*ma_y
                        ma1_y=1.1*ma_y-.1*mi_y
                        isocline1=implicit_plot(x==f, (x,mi1_x,ma1_x), (y,mi1_y,ma1_y),legend_label='iso1',rgbcolor='orange')
                        isocline2=implicit_plot(y==g, (x,mi1_x,ma1_x), (y,mi1_y,ma1_y),legend_label='iso2',rgbcolor='brown')
                        graf = graf + isocline1 + isocline2
                show(graf,frame=True,axes=False,axes_labels=['$x_n$','$y_n$'])
    if parameters=='4':
        @interact
        def _(paramint1=input_box(label='Slider interval for paramater $a$',default=(0,10),width=20),
             paramint2=input_box(label='Slider interval for paramater $b$',default=(0,10),width=20),
             paramint3=input_box(label='Slider interval for paramater $c$',default=(0,10),width=20),
             paramint4=input_box(label='Slider interval for paramater $d$',default=(0,10),width=20)):
            @interact#(layout=dict(bottom=[['param1'],['x0'],['y0'],['iterasyon'],['figs']],top=[['f'],['g'],['segment_check'],['isoclines_check']]))
            def _(
                param1=slider(paramint1[0], paramint1[1], .05, default=(paramint1[0]+ paramint1[1])/2,label='$a$'),
                param2=slider(paramint2[0], paramint2[1], .05, default=(paramint2[0]+ paramint2[1])/2,label='$b$'),
                param3=slider(paramint3[0], paramint3[1], .05, default=(paramint3[0]+ paramint3[1])/2,label='$c$'),
                param4=slider(paramint4[0], paramint4[1], .05, default=(paramint4[0]+ paramint4[1])/2,label='$d$'),
                f=input_box(label='$f(x,y)$',default=x+(1-a)*sin(y/b),width=40),
                g=input_box(label='$g(x,y)$',default=c*cos(x/d),width=40),
                x0=slider(intx[0], intx[1], .05, default=(intx[0]+intx[1])/2,label='$x_0$'),y0=slider(inty[0],inty[1], .05, default=(inty[0]+inty[1])/2  ,label='$y_0$'),
                iterasyon=input_box(default=100,label='Number of iterations',width=12),
                segment_check = ("Joined Points", True),
                isoclines_check = ("Show Isoclines", False),figs=slider(2, 20, 1, default=5,label='Figure size'),
                ar=slider([2^s for s in [-10..10]], default=1,label='Aspect Ratio' )
            ):
                f=f(a=param1,b=param2,c=param3,d=param4)
                g=g(a=param1,b=param2,c=param3,d=param4)
                nok=[(x0,y0)]#list of points
                for i in range(iterasyon):
                    nok.append((f(x=nok[i][0],y=nok[i][1],a=param1,b=param2,c=param3,d=param4),g(x=nok[i][0],y=nok[i][1],a=param1,b=param2,c=param3,d=param4)))
                    graf_nok=point(nok,frame=False,rgbcolor='black', pointsize=10,figsize=figs,aspect_ratio=ar)#, legend_label='origin')
                    graf_ilk=point(nok[0],rgbcolor='green', pointsize=40)
                    graf_son=point(nok[-1],rgbcolor='red', pointsize=40)
                    graf_segments=list_plot(nok, plotjoined=True, color='purple',alpha=.3)
                    graf=graf_ilk+graf_son+graf_nok
                    if segment_check:
                        graf = graf + graf_segments
                    if isoclines_check:
                        nok_x= [nok[i][0] for i in range(len(nok)) ]
                        mi_x=min(nok_x)
                        ma_x=max(nok_x)
                        nok_y= [nok[i][1] for i in range(len(nok)) ]
                        mi_y=min(nok_y)
                        ma_y=max(nok_y)
                        fark_x=ma_x-mi_x
                        fark_y=ma_y-mi_y
                        mi1_x=1.1*mi_x-.1*ma_x
                        ma1_x=1.1*ma_x-.1*mi_x
                        mi1_y=1.1*mi_y-.1*ma_y
                        ma1_y=1.1*ma_y-.1*mi_y
                        isocline1=implicit_plot(x==f, (x,mi1_x,ma1_x), (y,mi1_y,ma1_y),legend_label='iso1',rgbcolor='orange')
                        isocline2=implicit_plot(y==g, (x,mi1_x,ma1_x), (y,mi1_y,ma1_y),legend_label='iso2',rgbcolor='brown')
                        graf = graf + isocline1 + isocline2
                show(graf,frame=True,axes=False,axes_labels=['$x_n$','$y_n$'])

Interact: please open in CoCalc