@Preben Alsholm It is amazing/sad how many different attempts were made at this problem without Maple giving any hint that there was a syntax error. The OP even thought that he was making progress towards a solution/fit.

@acer It is not clear to me whether the intended operation was `*` or `/`, but clearly some operator is needed.

@brian bovril The benefit of using an iterator, such as from the Iterator package, is that you can quit before you've generated all the partitions.

@J F Ogilvie What exactly did you have to do to get it to work? It would be nice to get you a higher-resolution graphic. What operating system are you using? Maybe changing jpeg to jpg would help.

Feel free to use the code and graphic, but please mention my name.

Note that the CodeTools:-Usage is just to print the timing and memory info. You can also get rid of the caption and maybe the axes.

Also check out this very simple fractal that I posted on New Year's Day 2013.

@J F Ogilvie The only thing I can think of is that the plotoptions is not working on your computer. You changed the file name for the output, right? Try removing the plotoptions line from the plotsetup command. If that doesn't work, then remove the entire plotsetup command (and do a restart) to see the plot inline and reduce the grid to [400, 400] or less (and be prepared to wait for the plot to render on your screen).

Let me know how that goes.

@brian bovril Since the minimum variation is about 38, you'll need to set your cut-off much higher than 0.021.

What book is algorithm 14.10 from?

Do you mean that you want to connect all 11 points as a polygon? or just the 5 points to the left of the vertical axis?

Could you repost the polynomials that the points came from?

Your code is missing.

@zy Your file did not upload. Could you try again?

@Markiyan Hirnyk Your procedure does not implement a variable damping. It just sets the damping factor to constant 0.25. Look at ODE before calling dsolve.

@Markiyan Hirnyk

One problem with using a procedure like above is that it only works for numeric arguments; non-numeric arguments will give an error. Also, piecewise expressions are fully supported as algebraic expressions. So, for example, a piecewise can be used as a coefficient in a differential equation.

@N00bstyle Yes, you are correct.

It's more realistic to base the change on speed rather than velocity. So I change the damping factor to use abs(diff(y(t), t) instead of diff(y(t), t). When I do this, the graph shows an interesting change in velocity where it otherwise would've gone below -0.2.

Download damping2.mw

@Kitonum I find the .~ a bit confusing---although it does work correctly---because this is elementwise scalar multiplication. So, you can just as well use *~.

@cesar torres The 8 is the number of bytes in the hardware floating point representation of the Matrix entries. This number can only be 4 or 8, 8 being "double precision".