### Materials and Methods

### Ethics statement

### Study design

*p*-value less than 5% probability of being normal and one with a

*p*-value less than 1% by pattern deviation, or (3) pattern standard deviation of less than 5%. Visual field defects were confirmed on two consecutive reliable tests (fixation loss rate of 20%, and false-positive and false-negative error rates of ≤25%). The control group was enrolled from subjects who had been referred as glaucoma suspect but had an intraocular pressure of ≤21 mmHg, a normal optic disc appearance, an open iridocorneal angle, normal red-free fundus photography, and a normal visual field.

### Optical coherence tomography angiography

*En face*images of the predefined Spectralis OCTA slabs were used for the analysis.

### Fractal dimension calculation

*N*is the number of objects,

*ɛ*is the linear scaling or magnification factor, and

*D*

*is the fractal dimension, which is equivalent to the inverse of the box’s linear dimension (Supplementary Fig. 1A-1C). The fractal dimension can be calculated by a log-log plot of*

_{f}*N*and

*ɛ*as follows:

*D*

*= log*

_{f}*N*/ log

*ɛ*(Fig. 1H) [24].

### Data analysis

*t*-test for the continuous variables and by chisquare testing for the categorical variables. The diagnostic utilities of parameters were determined by calculating the areas under the receiver operating characteristic (ROC) curves (AUCs). The ROC curve shows the trade-off between sensitivity and specificity. An AUC of 1.0 represents perfect discrimination, whereas an AUC of 0.5 represents chance discrimination. The following established five-category rating scale was used for interpretation of AUC values: >0.90, excellent; 0.80-0.90, good; 0.70-0.80, fair; 0.60-0.70, poor; and 0.50-0.60, fail [27]. Univariable and multivariable analyses were run to determine the factors associated with fractal dimension, and parameters with a

*p*-value less than 0.10 in the univariable analysis were included from the subsequent multivariable analysis. Statistical analyses were performed with commercially available software (Stata ver. 16.0; Stata Corp., College Station, TX, USA). The data herein are presented as mean ± standard deviations except where stated otherwise, and the cutoff for statistical significance was set to

*p*< 0.05.

### Results

*p*< 0.001) (Fig. 2A), whereas it did not correlate with that of AVC (r = −0.010,

*p*= 0.922) (Fig. 2B). In POAG eyes, the fractal dimension of SVC decreased as the average RNFL thickness decreased according to disease severity (Fig. 3A-3I). The glaucoma-diagnostic utility was excellent for the average RNFL thickness (AUC, 0.889; 95% confidence interval [CI], 0.825-0.953), and good for the fractal dimension of the SVC (AUC, 0.772; 95% CI, 0.675-0.870). The AUC difference was statistically significant (

*p*= 0.008) (Fig. 2C).

*p*< 0.001) (Fig. 2D) and AVC (r = 0.817,

*p*< 0.001) (Fig. 2E). The glaucoma-diagnostic utility of SVC vessel density (AUC, 0.778; 95% CI, 0.683-0.874) was not statistically different from that of the SVC fractal dimension (

*p*= 0.557) (Fig. 2F).

*p*< 0.001) and with shorter axial length (

*p*< 0.001) and thicker average RNFL thickness (

*p*< 0.001) (Table 2). The fractal dimension of the AVC, meanwhile, was higher in subjects with larger BMO area (

*p*= 0.013, Table 3).

### Discussion

*ɛ*increases, and the number of boxes (

*N*) increases reciprocally. In the pattern with self-similarity-like vessels, the slope of their changes converges to the fractal dimension. As arborizing structures, the vessels are very suitable for evaluation of the fractal dimension. In contrast to density, the fractal dimension is unaffected by the size of the surface plane, and thus it has the potential for more robust parameters of vascularity. The fractal dimension has been used for evaluation of macular vascularity in diabetic retinopathy [12], hypertensive retinopathy [17], and age-related macular degeneration [16]. In POAG, the fractal dimension has been used for evaluation of ONH vascularity as measured by Heidelberg Doppler flowmetry [18]. To the best of our knowledge, however, fractal dimension analysis was not used to evaluate the layer-by-layer vascularity of the ONH and peripapillary area, which has been possible only since the recent advent of OCTA.