The class feature "story" block for this feature is somewhat vague as to what it exactly is. It does say it's a magical construct, so would you just snap your fingers and poof? Throw down a box that morphs into the turret? Suggestions are welcome.

My artillerist has a system of discs that counter rotate around a gear that keeps them locked in place.

When thrown out like a frisbee, the gear spins, unlocking the discs causing them to rotate into a ball that maintains it balance using gyroscopes. The outer edge of the "ball" contains a sticky like substance that allows it to even climb up walls and ceilings.

Within the center is an arcane prism that eminates specific arcane powers depending on the type of turret used. Red for Flamethrower, Blue for Force and Green for defense.

Honestly it is up to the player, really. The Artificer is the most fluid class when it comes to fluff like this.

Mine has a bunch of little wind up toy soldiers.

I was going to have my turrets, be a series of 4, 1 inch thick, 6 inch diameter, discs (think, old film real containers).

Each disc would have one side with a locking mechanism and the other would be a closed mechanical iris (think star-gate irises). The discs would be small compressed space (IE extra dimensional space) canister, with a magical/mechanical payload inside.

Then, whenever my character would summon a turret, he would first grab the disc labelled (or coloured?) as the base and which ever of the other 3 discs, depending on what turret he was trying to summon. He would then slap the base and top together and twist lock them to each other and throw them out. As they are falling, the irises on the 2 discs would open and out of the base would unfold 4 magical/mechanical spider like legs, and out of the top would unfold the magical/mechanical delivery system (different depending on the type).

So they would have a upper contraption of mechanical and magical artifice, a base of 4 spider-like mechanical and magical legs, and a small neck/rotate join, in the middle.

Mine were classic though I did make each one distinct.

The Force Cannon I literally just took the concept of particle acceleration and had atoms spin around before being released towards the target. The design could be equaled to an automatic tennis ball machine with a gumball machine where the particles spin around.

The flamethrower i had with a flat side with many tiny holes. Blisters and sparks are shot out from the holes at high intensity, but disappearing with distance. It has some inspiration from rocket launcher turrets only flatter.

The Guardian effectively looks like a vertical air conditioner only bulkier. The energy it releases is slightly cool but offers no mechanical advantage.

A thing to note is that as the class meant to imagine and fluff extensively, there is little limitation on creativity. The turret could easily be more biological or even arcane in nature so long as it functions as one of the three turrets and has spider legs.

Example: the force cannon can be Ocula from the Small Soldier movie, just shooting a force beam from it's eye. The Guardian can be a Heart being carried in a glass sphere, its palpitations giving the extra hit points. The Flamethrower can be a captured lesser fire elemental trapped inside some contraption.

The last one is a bit evil, but flavorful!

I Flavored mine by making it a Tin Top Hat. With a smoke stack and various rivets and gears. I take the hat off and use my tool to select the turret type. It then transforms with the hat brim seperating and folding down to create the "crablegs". When it Explodes or is destroyed it pulls itself back together i.e. The Golden Army bots from Hellboy2.

I decided to just go with the morphing boxes idea.

The 5 sides (all except the underneath) extend out and angle themselves to look like tank armour while the legs and turret pop out. The Flamethrower is a red box and is the smallest - it turns into an angry chittering spider with a small nozzle turret. The Ballista a bigger grey box and turns into something more like a turtle with 4 chunky legs to support the force of the attack and the turret is more like a sniper rifle's barrel (long like a turtle neck). The protector is a blue sphere and it just rolls itself around and just creates a shockwave pulse of energy from its casing instead of having a turret.

My artillerist has an extra set of wands. They grow spider-like wooden legs when he needs them to move around or cling onto something.

I thought about modeling a Turret after Bolt, the Superdog! Then my character could say “Bolt. Speak.” And unleash the Superbark!! (It would be totally, fully awesome! I’ll get my ball.)

My arty is a farmer that made a bunch of constructs to help around the farm.  Her force cannons are a pair of clockwork chickens that bend over and fire eggs that explode.

A tiny metal version of the Artificer.

Works particularly well if the Artificer is a bit of an eccentric egomaniac.