Abstract: In this study, we draw on fractal dimension theory and employ the edge-to-area ratio to quantify geometric complexity. Additionally, we introduce a method for calculating geometric complexity based on rotational self-similarity and conduct comparative research based on these two complexity definitions. Furthermore, we examine the quantitative relationships between geometric complexity, reconstruction accuracy, and the number of projection angles using these two methods of complexity calculation. The resulting quantitative models offer insights into the reconstruction accuracy of random geometries from few projections and establish the minimum number of projection angles required to achieve a predetermined level of reconstruction accuracy.