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Is there a term for a condition or inclination of only sleeping on an as-needs basis? (analogous, perhaps, to hydration habits, where some people may have a regular pattern for when they drink water, but others may only do so on an 'as needs' basis e.g. whenever they feel thirsty)

Another analogy: eating. Some people eat on a very set schedule (e.g. 3 meals a day), but others eat whenever they're hungry. I wonder if some perfectly normally functioning people sleep in the same way the latter of the aforementioned eat, that is, when they feel they need it, rather than on any predetermined schedule.

A can find segmented sleep, which still seems organised, but into 2 segments per 24 hour period rather than the more common 1 segment.

But I am looking at something a bit different, where the person simply sleeps as they feel they require it (other activities permitting). For example, someone with this sleep habit might sleep for 8 hours, stay up for 20, sleep for 4, stay up for 12, sleep for 10, stay up for 16, sleep for 4, stay up for 3, sleep for 2, stay up for 13. If we study the data for how humans consume food or water, we should find many who consume in similarly highly irregular and unpredictable patterns, yet would be considered completely normal people. Does the same exist for sleep?

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As far as I know, there's no medical term for a person who does such a thing (and I doubt it would be labelled a disorder since practically everyone can do it to some extent), but the 2nd part of the act that you're talking about (i.e. sleeping longer after a shorter/insufficient sleep before) is often called recovery sleep, while the term for the first part is much more broadly know, i.e. (partial) sleep deprivation. I wrote a more extensive answer to a question on the effects/efficacy of recovery sleep on Psychology SE, which has a bunch of references.

Also on this theme, you may be interested in a review on daily intraindividual variability of sleep/wake patterns

Features of an individual's sleep/wake patterns across multiple days are governed by two dimensions, the mean and the intraindividual variability (IIV). The existing literature focuses on the means, while the nature and correlates of sleep/wake IIV are not well understood. A systematic search of records in five major databases from inception to November 2014 identified 53 peer-reviewed empirical publications that examined correlates of sleep/wake IIV in adults. Overall, this literature appeared unsystematic and post hoc, with under-developed theoretical frameworks and inconsistent methodologies. Correlates most consistently associated with greater IIV in one or more aspects of sleep/wake patterns were: younger age, non-White race/ethnicity, living alone, physical health conditions, higher body mass index, weight gain, bipolar and unipolar depression symptomatology, stress, and evening chronotype; symptoms of insomnia and poor sleep were associated with higher sleep/wake IIV, which was reduced following sleep interventions. The effects of experimentally reduced sleep/wake IIV on daytime functioning were inconclusive. In extending current understanding of sleep/wake patterns beyond the mean values, IIV should be incorporated as an additional dimension when sleep is examined across multiple days. Theoretical and methodological shortcomings in the existing literature, and opportunities for future research are discussed.

As you can see, a more persistent pattern of such intraindividual variability can be linked to some sleep disorders. However, the review also discusses the extent to which this correlation may be misinterpreted, i.e. proposes that some IIV may actually be adaptive/beneficial:

despite more variable sleep/wake patterns being associated with a range of adverse outcomes, it is not clear that greater sleep/wake IIV is always related to deleterious outcomes, or whether such associations are linear. In different contexts, greater IIV can be theorized as being both non-adaptive and adaptive [71]. For example, much has been said about irregular sleep as a non-adaptive behavior in the context of insomnia, with the implication that regular sleep is adaptive. However, very low variability in sleep timing among patients with insomnia sometimes stems from rigid rules about sleep timing that are anchored in a general maladaptive belief that sleep is fragile or there is a critical window for sleep. Moreover, a finding that healthy irregular sleepers were less prone to microsleep after sleep deprivation [57] suggests that these individuals might adapt better to changing sleep durations.

[citing for that para:]

[71] Roecke C, Brose A. Intraindividual variability and stability of affect and wellbeing. GeroPsych 2013;26:185-99.

[57] Innes CRH, Poudel GR, Jones RD. Efficient and regular patterns of nighttime sleep are related to increased vulnerability to microsleeps following a single night of sleep restriction. Chronobiol Int 2013;30:1187-96.

On the matter of terminology, the review says:

inconsistent terminologies (e.g., “night-to-night variability”, “daily variation”, “daily instability”, “day-to-day fluctuation”) have been used to describe IIV of sleep/wake patterns. A consistent terminology across future studies will help enhance coherence of this literature and improve the access of relevant findings. For this purpose, we recommend “intraindividual variability (IIV)”

Also, there isn't a lot of agreement how exactly to measure the day-to-day variation, while also taking into account the external constraints that may vary from day to day (e.g. workday vs free day). Various metrics have been proposed; see section 3 in a fairly recent (2018) review by Vetter.

To point to a fairly intersting recent paper (that happens to be open access) as an example in this area, see Phillips et al. (2017). In their paper they use "irregular sleeper" for someone exhibiting such pattern, if they are in the bottom quintile in their Sleep Regularity Index, defined as:

This index calculates the percentage probability of an individual being in the same state (asleep vs. awake) at any two time-points 24h apart, averaged across the study. The index is scaled so that an individual who sleeps and wakes at exactly the same times each day scores 100, whereas an individual who sleeps and wakes at random scores 0. This index is constructed on the reasoning that changes in sleep schedules from one 24-h interval to the next may cause circadian disruption and thus impact normal biological functioning and health. The SRI differs from previous approaches in that it does not require designation of a main daily sleep episode, and can thus be applied in populations such as college students, where additional daytime sleep episodes and all-nighters are commonly observed.

Of course, since this is a fairly recent paper, one can only guess if the terminology (or their way of measuring sleep irregularity) will gain widespread acceptance.

And the the lead author of that paper is a co-author of another one (2019) that contrasts it to a different (recently proposed) metric:

Two metrics have been recently developed to specifically capture day-to-day changes in sleep patterns: the Composite Phase Deviation (CPD [24]) and the Sleep Regularity Index (SRI [9]). The CPD metric combines sleep irregularity and sleep mistiming by quantifying (i) how different the mid-sleep times are compared to those on the previous day, and (ii) how far away mid-sleep times occur from an individual’s preferred sleep timing (chronotype, as measured by midsleep time on weekends [25]). The SRI calculates the probability of an individual being in the same state (asleep vs. awake) at any two time-points 24h apart, scaled to values between 0 (completely irregular) and 100 (completely regular). While CPD and SRI both capture day-to-day changes in sleep patterns, CPD may be complementary to SRI due to its composite nature, combining features of irregularity with mistiming. For example, in shift work, sleep during the daytime for several consecutive night shifts tends to be highly regular (as captured by SRI and the irregularity component of the CPD metric) but as it occurs during the day it is largely mistimed for the majority of shift workers [26]. This mistiming is captured by the second component of the CPD metric but not by the SRI.

As the Vetter review (had) noted, this field of research is still evolving fairly rapidly.

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