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How do I create a multiple tree of the differences of a numerical sequence?

Kevin Teal
Posted 11 years ago

I'm new to Mathematica and on WolframAlpha when you input a short number sequence you'll usually get a nice differences tree, showing the differences of each level of differences. I was wondering how to get this same multi-level tree of the differences in longer numerical sequences on Mathematica? (instead of just one level at a time)
POSTED BY: Kevin Teal
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Kevin Teal
Kevin Teal
Posted 11 years ago

You're right, it works fine on Mathematica... thanks, I really appreciate it, it's awesome!

Is there a way though, to make it so that the actual sequence itself appears as the first line in the Output?

POSTED BY: Kevin Teal

Copy my second code.
POSTED BY: Sander Huisman
Kevin Teal
Kevin Teal
Posted 11 years ago

Sorry, didn't realize that. Thanks, Sander, I really appreciate your help. Have a great holiday!
POSTED BY: Kevin Teal
Kevin Teal
Kevin Teal
Posted 11 years ago
POSTED BY: Kevin Teal
POSTED BY: Sander Huisman
Kevin Teal
Kevin Teal
Posted 11 years ago

That looks awesome, almost perfect, except that I want the original sequence to appear as the first line... how do I do that? (obviously completely new to Mathematica)

Still though, when I copied it to try it, I got this result:

SetDelayed::write: Tag Times in Null xypos[xsList,y] is Protected.

It didn't come out.
POSTED BY: Kevin Teal

If i copy the above it works fine, clear your Memory (or restart mathematica) to be sure...

here is it with the original sequence:

ClearAll[xypos]
xypos[xs_List, y_] := MapThread[Text[#2, {#1, y}] &, {2 Range[Length[xs]] - Length[xs], xs}]
seq = {1, 2, 3, 4, 10, 19, 36, 69, 134};
seqs = Differences[seq, #] & /@ Range[0, Length[seq] - 1];
heights = Range[Length[seqs], 1, -1];
Graphics[MapThread[xypos, {seqs, heights}]]
POSTED BY: Sander Huisman
Kevin Teal
Kevin Teal
Posted 11 years ago

Does anyone know how to produce a differences to multiple levels (like the above example from WolframAlpha) on Mathematica? I can sort of produce it, but not in the elegant way it looks above...
POSTED BY: Kevin Teal
Kevin Teal
Kevin Teal
Posted 11 years ago
POSTED BY: Kevin Teal

I was not able to figure out what you did in Wolfram|Alpha (a specific example is always helpful). Possibly this will give a start along the lines of what you want.

aa = {1, 81, 28, 13, 19, 57, 25, 87, 19, 44};
NestList[Differences, aa, 3]

(* {{1, 81, 28, 13, 19, 57, 25, 87, 19, 44}, {80, -53, -15, 6, 38, -32, 
  62, -68, 25}, {-133, 38, 21, 32, -70, 94, -130, 93}, {171, -17, 
  11, -102, 164, -224, 223}} *)

This variant will go all the way to the root, so to speak.

Most[FixedPointList[Differences, aa]]

 (*  Out[37]= {{1, 81, 28, 13, 19, 57, 25, 87, 19, 44}, {80, -53, -15, 6, 
    38, -32, 62, -68, 25}, {-133, 38, 21, 32, -70, 94, -130, 
    93}, {171, -17, 11, -102, 164, -224, 223}, {-188, 28, -113, 
    266, -388, 447}, {216, -141, 379, -654, 835}, {-357, 520, -1033, 
    1489}, {877, -1553, 2522}, {-2430, 4075}, {6505}, {}} *)
POSTED BY: Daniel Lichtblau
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