Where/when does the wok start to differentiate itself from pot-style cooking vessels?

Question

I can understand how basic pottery imitating gourds can lead to "cauldron" style hanging pots, and on to the modern shapes used predominantly in the west. Similar for the flat cooking surfaces from stones to modern pans.

But how & where did all this branch off to the large(-ish) concave vessels predominant in Asian cultures? After all this isn't really a shape readily available in nature as a cooking surface to imitate. So what made people switch over to this particular shape?

The History section on Wikipedia doesn't give a lot of information, and the page on "History of the Wok" does give theories as to why it was invented, but not Why this specific shape.

Answer 1

The Chinese word itself from which we borrowed our concept of this implement seems to be much older than the actual pan/pot we understand this utensil to be now.

The frying/cooking methods this present gadget was used for are also older — roughly Han dynasty (206 BC–220 AD) — than for the modern form pan.

It seems that indeed only during Ming times (1368–1644) all factors needed to define the present day wok (that we associate with it) solidified:

• roughly the present day shape and
• usage scenario and methods (mainly quick cooking/frying in plant-based oils, previously animal fats, especially in the North).
• actual word used for exactly the above two bullet points

There were two main types of cooking pot in prehistoric and ar­chaic China—those with legs (of which the round or rectangular ding [caldron] was the most important) and those without legs (of which the round-bottomed, multi-purpose fu was the main one). The fu was remarkably similar to the modern deep pot (shenguo), or caldron pot (dinguo). These had no legs because they were designed to sit in the round aperture that formed the top of a small portable stove that was itself simply a pot with a square hole at the side (used as a door for the draft and the extraction of ashes […]).

The fu was a boiling, stewing, steaming, and frying vessel. It was much used in the Han, which saw the widespread production of relatively thin­ sided cast-iron fu.

By the end of the dynasty, the word huo (a similar vessel and possibly also a dialect character) was used in place of fu. Soon huo was replaced by guo (the all-purpose word for cooking pot，which remains in use today).

In Cantonese and various other southern dialects guo is still written as huo (pronounced 'wog,' not too distant from the ancient reading of both huo and guo).

Wog is, of course, the origin of the English word “wok.” Two-handled woks made of cast iron were common in the South. They were called erguo. Single-handled woks made of wrought iron were more common in the north. The name for them today is chaoshao (Stir-fry pan).

It took many centuries before the iron fu, huo, and guo gradually came to resemble todays wok.

Therefore, statements such as

“the wok has been used in Chinese cookery for at least 2,000 years”

are misleading, because although the word may have been in use for about 1,800 years, the vessel of that name changed both in shape and in use.

Indeed, it was only by the Ming that the sides of the guo had shrunk to the proportions of the modern wok (a high-sided fry pan with a rounded bottom, similar in form to the Indian dekchi).

Up to this time, the guo (wok), like its predecessor the fu, was used to cook dishes by all kinds of different methods. If it was used for stir-frying，it was mainly to parch (huogan) grains (just as Tibetans to this day parch qingke barley flour, the first step in preparing rtsam-pa (zaanba). The guo was used for roasting tea leaves, or for preparing dishes sequentially in combination with other cooking methods.

— Endymion Wilkinson: "Chinese History. A New Manual", Harvard University Press: Cambridge, London, 2013, p459. (Chinese characters removed & paragraph formatting adapted)

Answer 2

I add some speculation re. the "So what made people switch over to this particular shape?" and "Why this specific shape" parts of the question here. The answer is based on stoves and pans as used in Mongolia. Of course Mongolia is not China, but they have a long history of cultural interaction and also use round-bottomed cooking vessels a lot.

Flat-bottomed cooking vessels are great if one has a flat surface to put them on. With modern stoves that is usually a given, but not necessarily if you go further back in time. Semispherical vessels on the other hand work well as long as you have three points where to base them on. E.g. three stones, different types of tripods or stoves with an opening above the fire, as long as that opening is roughly as wide as it is long.

Re. tripods, the only free image that I found is this one:

(from Pallas, Samlungen[sic] historischer Nachrichten über die mongolischen Völkerschaften, St. Petersburg 1776, vol.1)

But there are images of a different (and I think more common) kind of tripod or quatropod here and here.

Open fire inside a house or yurt has two major problems, which are smoke and the risk of burning down your home, so people will prefer closed stoves over open fireplaces. Closed stoves in Mongolia and also rural China usually come with a circular opening in the upper surface, which is a perfect fit for a round-bottomed cooking vessel. Some images from China here, but if anyone finds a free one, I would like to include it here. This is a rather crude version from Indonesia to give an idea (source)*:

As indicated in a comment below the other answer, a round hole is obviously a good fit for a round-bottomed cooking vessel. But it is equally obvious that a round hole can be covered by a flat metal sheet, so the round-bottomed shape is not strictly necessary for being able to use a Chinese-style cooking stove. But it does not hurt either.

As an aside, stoves with circular openings in the upper surface were once common in Europe too (image source):

My guess is that a larger circular opening means that the heating power of the stove is larger (the food gets hot quicker). If that is true, putting a flat-bottomed cooking vessel on a metal sheet would be less effective than putting a round-bottomed cooking vessel onto a circular opening on a cooking stove.

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*Stoves in rural China seem to be mostly made from brickwork, while stoves in rural Mongolia are overwhelmingly made from iron.