Normally, embryos form 4 limb buds, 2 anterior & 2 posterior.

If you cut an early limb bud in two, it can form 2 arms, or often it will form a branched leg (mirror images).

Fusing two limb buds can often form only one leg.

Notice these similarities to splitting early embryos!
Some parts of embryos develop as coherent fields.

Some parasitic worms split limb buds in frogs,
resulting in 5 or 6 hind limbs! (picture on page 525)

Surgical grafting of olfactory placodes, or inner ear placodes, to the side of an animal between the front and hind legs will cause the tissue there to "grow" (reorganize) into a fifth leg!

Another way to cause formation of extra legs is by surgical insertion of beads soaked in fibroblast growth factor. ("FGF", which is a certain protein).

People think probably that grafted olfactory placodes, etc. produce their effect by secreting FGF, but perhaps that's an over-simplification

Development of the 3 geometric axes are controlled separately.

Proximo-distal
Anterior-posterior
Dorso-ventral

The Apical Ectodermal Ridge (AER) is a thickening of the epidermis that forms along the outer rim of the limb bud.

Surgical removal of the AER causes failure of the distal structures to develop.
Cut the AER off early, then no elbow, forearm, wrist or hand.
Cut the AER off later, then no wrist & hand.

Grafting an extra AER can cause a double wing to form.
A mutation in chickens causes double AERs and double wings!

But the AER doesn't itself become any these structures. It somehow signals to them to form.
There has been much research and several theories on this subject

Fibroblast growth factor 10 seems to be the key signal molecule. FGF10 can replace the effect of the AER; If you cut off the AER, & put a bead coated with FGF in its place then the distal limb structures will form more or less normally.

Nobody (but me) wonders why the AER cells are a special shape. Does their shape mean they are more contractile, or what? In teleost fish, there is a fin-fold at the location of the AER; and also another fin-fold along the back and tail.

The proximo-distal axis is considered to be controlled by the AER

The anterior-posterior axis can be reversed by grafting cells from the back side of the limb bud to the front side, which is called the "Zone of Polarizing Activity" (ZPA)

What is the chemical basis of this? Is it retinoic acid?
Mirror-image branching legs can be produced by putting retinoic acid onto the anterior side of an early limb bud.

And if you put RA on the regenerating tail stump of a frog, then one or several legs will grow instead of a new tail!

And putting RA on the regenerating leg stump of a salamander will cause the entire proximo-distal sequence of structures to be regenerated, even if only the hand or wrist had been cut off!

The newer evidence is that the sonic hedgehog protein controls the anterior-posterior axis formation.

Organization of fingers somehow depends on hoxD 9, 10, 11, 12, 13

The spaces between fingers are made by programmed cell death
= "apoptosis" activation of cytoplasmic enzymes, that digest cells from the inside out.

The webbing of a ducks foot results from a lack of apoptosis.

And by the way, many cancer chemotherapy drugs actually work by stimulating apoptosis, rather than by direct harm!!

The dorso-ventral axis of limb development:

Can be reversed by removing the entire limb bud ectoderm and turning it upside down.

The key protein is thought to be one of the Wnt protein.