Need advise/suggestions for filling gaps in rough wood exterior walls.

I am currently in the process of planning a tinyish house build. My current plan is to use round end cuts from a cedar tree processer(I can get a trailer load for $150) as a exterior siding. Being that they are irregular cuts and may not line up well I was wondering if there is a good method of filling those gaps without have to worry about degridation and water leakage into the inner wall s.

That sounds heavy,  so I hope you are not planning for your house to be mobile.
In any case,  I would use more of the rounds themselves.
Like shiplap or cedar shakes only irregular.
How are you intending to attach them?
What will be underneath them?
I think most siding is only a first line of defense against water.
In part,  the siding defends the actual water and air infiltration barriers from sun and wind.

It's not going to be mobile. I was planning on attaching the wood to the 2x4 frame via screws or possibly nails depends on what I can get my hands on. I was hoping to do in the style of old pioneer houses that have the wood planks with some mud type substance in between. But in my research I have failed to find any specifics on what the muds substance consists of. I thought it was possibly cob or a clay based plaster. Keep in mind I live in an area with very mild winters so Im toying with the idea of leave the walls without insulation and heating the house via a rocket mass heater.

A 2x4 frame usually has studs every 16 inches.
How wide are these rounds?
Are you thinking of infilling between the studs?

These aren't rounds they are the rounded edges left over in the production of planks.  I apologise if I wasn't clear enough initially. They boards I've gotten in the past they vary from 4'-8' long and 4"-8" wide.

Screw them to the wall studs and stack them up just like it was a log cabin.  Put 2 of them together vertically along the corners and then chink in between each row with Permachink or Logjam.  Both commercially available products specifically for log building applications.  This pic is an interior wall of my house that is sided exactly that way but used cheaper painters caulk instead of permachink for the chinking.each row was trimmed to the same size so there was no alternating of tip, butt ends like a normal log wall.  A draw knife helped make everything line up nice.  This interior trim used finish nails, but outside I’d just use some 6-8 inch hex head log screws.  They have a long smooth shank with the screw threads only being a couple inches long.

T Hayden wrote:Screw them to the wall studs and stack them up just like it was a log cabin.  Put 2 of them together vertically along the corners and then chink in between each row with Permachink or Logjam.  Both commercially available products specifically for log building applications.  This pic is an interior wall of my house that is sided exactly that way but used cheaper painters caulk instead of permachink for the chinking.each row was trimmed to the same size so there was no alternating of tip, butt ends like a normal log wall.  A draw knife helped make everything line up nice.  This interior trim used finish nails, but outside I’d just use some 6-8 inch hex head log screws.  They have a long smooth shank with the screw threads only being a couple inches long.

I appreciate your response it's nice to see an example similar to what my plan was.

Ah,  I see!
People call that slab wood sometimes.
I think I would wrap the frame in tarpaper or some kind if housewrap,  then add diagonal  2x furring on top of that.
To attach  the slabs to the furring,  I would use  deck screws and run them vertically.
Vertical wood siding is said to last longer.
To cover the gaps,  I would use more slabs,  shiplap style.
The furring would provide an air gap between the siding and water resistant barrier.