x,y,a=var('x y a')
@interact
def _(
param1=input_box(label='Slider interval for paramater $a$',default=(0,10),width=20),
intx=input_box(label='Slider interval for $x_0$',default=(0,10 ),width=20 )):
@interact
def _(
f=input_box(label='$f(x)$',default=x*e^(a-x),width=40),
x0=slider(intx[0] , intx[1], .1, default= (2*intx[0]+intx[1])/3 ,label='Initial Value $x_0$' ),
parameter0=slider(param1[0] , param1[1], .01, default= (5*param1[0]+param1[1])/6 ,label='Parameter $a$' ),
iterasyon=input_box(default=100,label='Number of iterations',width=15 ),
figs=slider(2, 20, 1, default=6,label='Figure size'),
ar=slider([2^n for n in [-10..10]], default=16,label='Aspect Ratio' )
):
f=f(a=parameter0)
nok=[x0]
for i in range(iterasyon):
nok.append( f(x=nok[-1] ) )
graf=list_plot(nok,plotjoined=True,rgbcolor='orange',aspect_ratio=ar,figsize=figs,axes_labels=['$n$','$x_n$'],frame=False)
show(graf)