{{{id=1| ##################### ###### Code Starts ## ##################### ##################### #Bifurcation Diagram #by Sinan Kapcak #2017 ##################### a,x,y=var('a x y') @interact def _( f=input_box(label='$f(x)$',default=x*e^(a-x),width=45), P0=input_box(default= n(.6,digits=3),label='$x_0$',width=15), parameter=input_box(default=(0,3),label='Interval for $a$',width=15),#,auto_update=False iterasyon=input_box(default=200,label='Quality Parameter#1',width=12),#number of iterations: 400 is good subint=input_box(default=200,label='Quality Parameter#2',width=12),#number of subinterval: 500 is good figs=slider(2, 20, 1, default=6,label='Figure size'), ar=slider([2^n for n in [-10..10]], default=1/2,label='Aspect Ratio' ) ): paramin=parameter[0] paramax=parameter[1] kk=(paramax-paramin)/subint paralist=[paramin+i*kk for i in range(1+subint) ] biflistx=[] for j in range(len(paralist)): nok=[P0]#list of points for i in range(iterasyon): nok.append(f(x=nok[i],a=paralist[j] )) if iterasyon < 200 : soniter = floor(iterasyon / 2) if iterasyon > 199 : soniter = floor(iterasyon * 2/5 ) nok_x=[ nok[-m] for m in [1..soniter] ] for mm in range(len(nok_x)): biflistx.append( [paralist[j] ,nok_x[mm]]) biflistgrafx=list_plot(biflistx, plotjoined=False, color='purple',alpha=.3,pointsize=1,figsize=figs,aspect_ratio=ar) graf=biflistgrafx show(graf,frame=False,axes=True,axes_labels=['$a$','$x_n$']) ##################### ###### Code Ends #### ##################### ///

$f(x)$

$x_0$

Interval for $a$

Quality Parameter#1

Quality Parameter#2

Figure size

Aspect Ratio

}}} {{{id=2| /// }}}