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I'm looking for a pair of adjectives which mean, respectively:

  • Fast/Frequently-changing
  • Slow/Rarely-changing

As an example usage:

Due to its everyday use, the balance of a current account can be quite fast-changing, but that of a savings account is more likely to be slow-changing.

And as a demonstrative graph: the value denoted by the red lines is more fast-changing, whereas the green value is a lot more slow-changing. The size of the changes is irrelevant - only the frequency is of importance.

Fast and slow changing graphs

The best I've come up with is volatile for the fast-changing part (probably closest to the third definition at dictionary.com), but I can't think of a suitable antonym. To me, stable has more of a connotation of not changing very much when it does change, as opposed to not changing very often.

By contrast:

Continuous graphs

If the green and red graphs above are frequently and infrequently changing respectively, then the orange, blue and purple graphs are changing continuously (infinitely frequently) - they're all way off to the "frequently" end of the spectrum.

  • Is the amplitude of change relevant as well? It is possible to have hell of a wiggling function where values are barely changing. – Arjang Nov 17 '15 at 9:35
  • @Arjang "The size of the changes is irrelevant - only the frequency is of importance.". Yes, a function which is constant for long periods before taking a massive jump to another value would be an example of "infrequently-changing". Likewise, a function which takes rapid, tiny steps would be a "frequently-changing" function. – Philip C Nov 17 '15 at 9:37
  • Specifically in the example usage, you could write "due to its everyday use, the variability of the balance of a current account can be high, but that of a savings account is more likely to be low. – MetaEd Dec 3 '15 at 18:37
  • In a more technical context, suggested by the first graph given, you might refer to pulse width. – MetaEd Dec 3 '15 at 18:48
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For your example, 'dynamic' and 'static' work:

Example: Due to its everyday use, the balance of a current account can be quite dynamic, but that of a savings account is more likely to be static.

dynamic adj.
...
3. Characterized by much activity and vigor ....

[dynamic. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved November 17 2015 from http://www.thefreedictionary.com/dynamic]

static adj.
...
3. showing little or no change ....

[static. (n.d.) Random House Kernerman Webster’s College Dictionary. (2010). Retrieved November 17 2015 from http://www.thefreedictionary.com/static]

  • I like dynamic, but I'm not quite so keen on static. Despite your given definition including "little ... change", if I saw something described as static, I wouldn't ever expect it to change. – Philip C Nov 17 '15 at 9:23
  • @PhilipC, yeah, I was thinking I'd like to rephrase the example: "... is likely to be more static." – JEL Nov 17 '15 at 9:27
  • Idiommatically, I suppose the pair active-idle doesn't suit your context? – JEL Nov 17 '15 at 9:28
  • Yep, that'd make it easier. Unfortunately, I really could do with an absolute adjective, not a comparative one. And no, they're both active things, one just changes far more often than the other (like the bank accounts, or the values on the graph). – Philip C Nov 17 '15 at 9:28
  • @PhilipC, along with active-idle, there's active-quiescent, active-lethargic. Other than active, lively, vital, productive are possible, each with their own oppositories. – JEL Nov 17 '15 at 9:35
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Abusing the term in mathematics :

Smoothness and $C^k$ seem relevant.

for example : Smooth or bumpy function.

  • What I'm after isn't really related to the continuity of the value - in the question both graphs are discontinuous step functions. If we're heading into mathematics, I'm looking for a pair of words that, given two step functions, would differentiate between the one with few step discontinuities and the one with many (ideally considering the x-axis as time). – Philip C Nov 17 '15 at 10:28
  • @PhilipC : yes, i know.However smooth function does conjure the image of not frequently changing, and bumpy function does. Hence misuse of mathematical term to fit something into everyday usage. – Arjang Nov 17 '15 at 10:33
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What about "stable" instead of "static"? I can see why "static" won't do - it usually implies that there is no change whatsoever - but "stable" often implies that change is possible.

So - "dynamic" and "stable".

0

There are great words here already for the quickly changing case. Also you can say up and down.

For the slowly changing case: boring, unchanging, steady, steady-going, slow moving.

Due to its everyday use, the balance of a current account can be quite up and down, but that of a savings account is more likely to be slow moving.

-1

We may use the terms "fluctuating-vs-consistent" in conformity with your example usage.

  • That would be for a different situation where some values are fluctuating and other values are constant. In the OP's situation, all the values are fluctuating. – MetaEd Dec 3 '15 at 0:02
  • Sorry for the spelling mistake. "Consistent" holds a balanced sense of variance as well. – Barid Baran Acharya Dec 3 '15 at 2:09

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