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I need to simulate & output the human heartrate BPM with real-world like values. I've been looking at a gaussian random approach but don't believe this fits my use case. I'm not concerned about the actual values only that they are uniformed & match the patterns of a monitored heart beat (i.e. increasing/decreasing uniformly)

the range is from 50-180 with linear increments/decrements with a single digit emitted every second e.g.

60,60,60,61,64,65,66,64,63,62,66,68,71,75,80,83,90,95..........

Any eloquent algorithms allow for this?

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    Maybe not. However, if you take measurements for different activitiy levels, you could attempt to use a best fit algorithm to derive the function you use for your average user. It really does depend on how you model the BPM in code though. – Berin Loritsch May 10 at 13:23
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they are uniformed & match the patterns of a monitored heart beat (i.e. increasing/decreasing uniformly)

Speaking as someone who uses a heart rate monitor, I think your understanding of how they work is incorrect.

First off, during steady-state activities the heart rate will remain in different fairly-narrow bands. For example, right now I'm sitting and typing, and my heart rate is 58 +/- 3; a few minutes ago I was walking around and it was 72 +/- 3. When I'm exercising it depends on speed and load: steady-state cruising on the bicycle might be in the 130-140 range, spiking to 165 during intervals or pushing up a hill (and from that you should be able to guess my age within 10 years).

So, I recommend that you first define some standard activity bands, and then define a timeline for transitions between those bands.

At any given second the heart rate would be a random value within the band (which should average to the center of the band). There's no need to get fancy here: a real-world heart rate monitor isn't that exact (particularly one in a wearable).

The transition between bands gets a little more interesting. I suspect that it follows a sine curve, although that very much depends on activity type (for example, when doing intervals I have a linear rise and sinusoidal decline). But if all you want to do is make a reasonable simulation, then I think that a linear transition would be sufficient.

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