If a city was able to hold markets, settlements often grew around a central market square (replace with Suq for Islamic cities). In many european cities, this (former) market square, often in combination with a representative religious building to show the prosperity of the city, is still the center of the city.
Some factors that differentiated a city from a village in Central Europe were:
- Market rights, staple rights and city rights. Market rights allowed a settlement to hold permanent, weekly or yearly markets and often (but not always) came together with city rights. These were often given by the nobility, e.g. the Holy Roman Emperor and elevated a town to a city. City rights gave cities a certain autonomy from local lords. Imperial (and free) cities were a special form of further autonomy and privileges under immediate reign of the emperor. A market gave major economic incentives to grow a settlement, city rights offered more freedom for immigrants. A german proverb is e.g. "Stadtluft macht frei" (city life makes you free), which alludes to you gaining your freedom from a lord if you lived in a city for a year and a day.
- The legal right, power and/or autonomy to have fortifications. This was sometimes, but not always given with city rights. This usually gave any settlement more practical autonomy from nearby nobility.
- Economic specialization, i.e. differentiation of labor from agriculture to various specialized trades. This required demand for those goods and a general economic surplus of the surrounding area.
- Differences in population: While today the difference of a city and a village is often based on population (e.g. 2.000 people as a treshhold in Germany), this wasn't necessary the case in medieval times. However, above a certain treshhold, any village was likely to gain either (1),(2) or (3), which further strengthened its economy, autonomy and defense and led to a higher population influx. But for the population to grow, there had to be a reason for this growth to happen to begin with.
So the market, legal rights (or the power to claim them, e.g. through sneakily building a wall) and an economic surplus was essential in the development from a village to a city. In an ideal development, this would move radially outwards from the market in all directions. In practice, riverbends, hills and other barriers usually dictated the direction of the growth of a city. Other than economic conditions, city walls often became an ultimate limit to city growth, as settlements outside the wall would destroy its defensive function and disallow line of sight. After a settlement reached its city walls, it could either create a new, wider set of walls or densify its existing structure inside the walls. The latter was the cheaper option up to a certain limit.
Many cities in central Europe only grew out of their city walls with the industrial revolution, a time in which walls became less functional and started to disappear. This often led to parks or major roads demarkating the old city from later structures on the position of the razed former city walls and the outlying glacis. They are often easily spotted due to their star-shape, based on the former Vauban-fortifications.
In some towns, a marketsquare-like opening already existed within villages, e.g. when they were built around a village green for grazing animals (see "Angerdorf in graphic below") or an elevated square (e.g. "Rundling"), which turned into a market square. The following graphic shows a few archetypal villagetypes of central europe, where this can be observed (Source: https://www.spektrum.de/lexikon/geographie/dorfgrundriss/1769):
