Fazlollah Soleymani
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 Mar 31 awarded Good Question Mar 31 awarded Yearling Mar 7 accepted Why doesn't FullSimplify work properly on this? Mar 7 accepted How to discretize a nonlinear PDE fast? Mar 7 accepted How could we define a function recursively? Mar 6 accepted How to introduce two successive points inside the FixedPointList for each cycle? Mar 3 comment How to introduce two successive points inside the FixedPointList for each cycle? What if we use the computations in multiple precision arithmetic, e.g. by applying 32 digits to avoid such cancellation and round off errors so as to draw the attraction basin for small $b$ as well? Mar 3 comment How to introduce two successive points inside the FixedPointList for each cycle? I cast doubt that in theoretic $b$ can be a small value, e.g $b=0.1$, but here we cannot draw its attraction basin! Why? Maybe, due to round-off errors! Mar 3 comment How to introduce two successive points inside the FixedPointList for each cycle? I got confused! It seems to me that your first response and also the response of JM (below) are better in the sense of final output fractal. There is no need to calculate the second point by another algorithm. Please choose $x_0$ as usual and $x_{-1}=x_0+0.001$ whenever the iteration is started. After starting, we have two values at each cycle (old one and the new approximation), clearly the new approximation replaces the old one but we keep both. Maybe, in this way, we could obtain a same final fractal for your approaches. Mar 2 comment How to introduce two successive points inside the FixedPointList for each cycle? Thanks. But I have a query. Why when we choose $b=0.1$, the code seems to break down and does not provide an attraction basin? How did you choose the two initial approximations ($x_{-1},x_0$) for converging to each fixed point? Mar 2 comment How to introduce two successive points inside the FixedPointList for each cycle? I tried to use it but I failed again. If you believe that it helps to finally draw the attraction basins with two seeds, please provide it in a complete answer. Mar 2 awarded Citizen Patrol Mar 2 asked How to introduce two successive points inside the FixedPointList for each cycle? Mar 2 answered Polar Decomposition Feb 29 accepted How to draw Fractal images of iteration functions on the Riemann sphere? Feb 3 comment How can we draw a stencil for discretization of PDEs? Wow. Thanks. The 3D plot is totally useful for showing the discretizations. Just one quick note. Usually, for the 2D case, the node left to (i,j) is (i-1,j) and the right one is (i+1,j). But here, it is vice versa. Although the plot is correct, I wished to know that how we can reverse this sorting of indices in the code. Feb 3 accepted How can we draw a stencil for discretization of PDEs? Feb 3 accepted How to find the index of a square matrix in Mathematica quickly? Feb 3 comment How can we draw a stencil for discretization of PDEs? I tried but I failed to build such a piece of code. Feb 2 comment How can we draw a stencil for discretization of PDEs? Thanks. I did as you suggested.