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.