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If you're interested in this type of paralyzing piece, then have a look on my Pyrrhus Chess. The Pyrrhus moves and captures like a king. In addition, it paralyses any enemy piece within queen-move range. It seems to be as valuable as a queen. 
http://hem.passagen.se/melki9/pyrrhuschess.htm
/Mats

The paralyzing Gorgona is implemented in Zillions here:
http://hem.passagen.se/melki9/gorgonachess.htm
The Gorgona is more powerful as it paralyzes pieces within queen range.
/Mats

What about a piece that imobilizes by moving AWAY

Would that mean other pieces could only move if they're within range of a hostile mobilizer?

No, it would immobilize similarly to the Withdrawer

It's still not clear what this means. A withdrawer captures by making a move, whilst an immobiliser stops others from making moves — the former's effect is on its own turn while the latter's is on the opponent's.

As such there's a couple of interpretations possible:

• It stops things from moving away like a withdrawer. This is just a weaker immobiliser, and is already attested in Euqorab
• It petrifies pieces that it moves away from rather than capturing them. Then the question is whether and if so when pieces can come back into play: never (as with Nemoroth's basilisk)? When the withdrawing‐petrifier moves again (leaving it able to only petrify one piece at a time)? After a larger but still fixed number of moves (turn counting, ugh)? Under some other condition? Are involuntary moves (from Swappers, shepherding pieces, Go Away!s, ⁊c.) counted? Does capturing it release pieces?

Imo the former option is not very interesting, nor necessarily well‐defined (how does it deal with knights?), while the latter is quite complex in principle and perhaps not very immobiliser‐like — though I admit the possibility of ulima‐style pieces with effects besides capture is interesting and not very well explored

It would stop immobilizing when it is no longer a queen's move away from that piece

I added an AI image of this piece in the form of a gorgon.

It misses the goal for me. It is not a chess piece at all. It is a figurine.

My favored representation of the Immobilizer is a (horse shoe) magnet. A simple shape, easy to recognize, easy to put on a pedestal to make it into a Chess piece, and a good mnemonic for something that holds other pieces in place.

For the coordinator I prefer a dish antenna, (or the more rectangular version used for radar, usually revolving), symbolizing action at a distance.

I've drawn a few ideas from this chart that someone did on DeviantArt, but not so much the Immobilizer. For that I put an octagonal figure at the top (and as a bonus I can add that figure to other pieces to create immobilizing versions).

As for the gorgon here, I agree with Jean-Louis; the pose and the base both say "figurine" rather than "chess piece."

Sounds good suggestions for both (answer to HG, for magnet and antenna dish)

It misses the goal for me. It is not a chess piece at all. It is a figurine.

There are figurine Chess pieces. So, being a figurine doesn't stop it from being a Chess variant piece.

My favored representation of the Immobilizer is a (horse shoe) magnet.

For the coordinator I prefer a dish antenna, (or the more rectangular version used for radar, usually revolving), symbolizing action at a distance.

Attempts to have the AI draw these as Chess pieces have not been successful.

I added another gorgon image. This one is a bust that would fit well with Peter Ganine's Superba/Gothic pieces or with the Musketeer Chess variant pieces.

You play with words. Of course, anything can be a chess piece, even 3 bamboo rods like in Pilipines. Figurines like in Warhammer can also be used to play chess but for chess and chess variants I think the best is Staunton-like pieces. Staunton's style is remarkable because it is at the good balance point between something purely abstract and very descriptive pieces like figurines.

I'm not playing with words. There are literally numerous figurine Chess sets being sold commercially. In contrast, I checked ebay for bamboo rod chess sets and didn't find any. I do share your preference for Staunton pieces, but for many Chess variant pieces, something more representational can be appropriate.

I added another gorgon image.

Either that wasn't successful, or something funny is going on: I only see the figurine image.

I don't think these images add much to these pages. I'd rather see them in a separate article. To the points about different piece sets/themes, you could aggregate similarly themed examples into a "set" article.

Refresh the page.

The newer images looks better to me. I don't know how you do these ai art things, but couldn't it be used to make 2d pieces for game courier?

I don't think these images add much to these pages. I'd rather see them in a separate article. To the points about different piece sets/themes, you could aggregate similarly themed examples into a "set" article.

I second this idea. A discussion on designing physical pieces for chess (both orthodox and fairy) would be a good idea, especially taking some of the thoughts that have been mentioned in this discussion. It'd be a lot of work sifting through images to find acceptable ones, but in the end I think it'd be worth it.

(Other things I wonder: How, in a one-color piece, does one show the difference between a Knight's horse and a Zebra, or a Leopard and a Tiger? How do I figure out how tall a piece should be? Stuff like that.)