The morphology of street patterns has been the subject of many studies in recent decades. While some have noted the textural and morphological differences in various parts of many cities, there have been few attempts to quantify the street patterns that contribute to these differences. For this study, we measured and compared the trends (orientations) and lengths of 4,266 streets in the old, historical part of the city of Yazd, Iran, and 4,021 streets in the new part of the city to quantify their textural (morphological) differences and similarities. In the old part of the city, the street trends are orthogonal and follow a normal (one-peak) distribution. The street lengths range from 4-317 m, follow power-law distributions, and yield street-population entropies of 1.360-1.565. The power-law distributions indicate that, in the old part of Yazd, there are many short streets and few long ones. By contrast, in the new part of the city, the street trends follow a bimodal (two-peak) distribution. The street lengths vary from 5-596 m, follow power-law distributions, and yield entropies of 1.632-2.290. All of the street populations show strong linear correlations between their scaling exponents, length ranges, and entropies, a finding that agrees with results from other cities. With regard to city planning, these correlations indicate that, as a city grows and expands, its street networks often increase in length and entropy, requiring greater energy for construction. The innovative quantitative approach used to analyze city textures in this paper can also be used to compare the sizes and shapes of buildings within and among cities.