We measure the Absolute Color Accuracy of the display with our proprietary sets of 41 Reference Colors for each Standard Color Gamut. The results are plotted on CIE 1976 Uniform Color Diagrams for each Gamut below.

41 Reference Colors for the wide DCI-P3 Color Gamut Standard
Figure 2a below shows 41 Reference Colors for the wide DCI-P3 Color Gamut as White, Gray, and Black circles. The 10 Black circles on the outer triangle are the 100% fully Saturated Colors on the periphery. The 3 inner sets of Gray triangles are the 25%, 50% and 75% Saturated Colors between the inner White Point and the 100% Saturated Colors on the periphery. The White circle is the White Point with 0% Color Saturation.

We have accurately calculated the Colors and Reference Colors for each of the iPhone 13 Pro Max Standard Color Gamuts: DCI-P3 and RGB / Rec.709. The colors in Figure 2a have been calculated to show the true colors within the DCI-P3 Color Gamut -- the colors shown in most published Color Gamuts are wildly incorrect. For an in-depth discussion and analysis of all the Standard Color Gamuts see this article.

Note that in order to see the true DCI-P3 colors in Figure 2a your display must support the DCI-P3 Color Gamut - if not then you will instead see the color saturation range that your display can produce, which in most cases will be lower than DCI-P3.

Figure 2a.   41 Reference Colors for the DCI-P3 Color Gamut Standard
Note that Complementary Colors lie directly across from one another through the White Point.
The 4 sets of triangles are the 25% 50% 75% and 100% Saturated Colors.

Uniform Color Diagrams
All color measurements are plotted on 1976 CIE Uniform Color Diagrams with (u',v') color coordinates.

Note that the older 1931 CIE Diagrams that are published by many reviewers with (x,y) color coordinates are highly non-uniform and are meaningless for Color Accuracy. Also the still widely referenced NTSC Color Gamut is from 1953 and has been obsolete for over 30 years so it is also meaningless for specifying the current Color Gamuts now in use.
For an in-depth discussion and analysis of Color Gamuts see this article.

Absolute Color Accuracy Plots
The iPhone 13 Pro Max has 2 Standard Color Gamuts.
Figure 2b below shows the measured on-screen colors for the sRGB Reference Colors.
Figure 2c below shows the measured on-screen colors for the DCI-P3 Reference Colors.

Reference Colors and Measured Colors
The Reference Colors in Figures 2b-2c are all shown as Black circles and the Measured Colors for the iPhone 13 Pro Max are shown as Red circles. Color Errors smaller than the appropriate JNCD are not visually noticeable. The 1 JNCD and 3 JNCD Errors are discussed next and are shown in the Figures below.

Just Noticeable Color Difference JNCD
The on-screen colors produced by any display can be measured using a Spectroradiometer together with our proprietary DisplayMate Test Patterns. The accuracy of the colors can then be calculated using the 1976 CIE Uniform Chromaticity color space and compared to the eye's sensitivity to color. We present the color accuracy and errors here in terms of MPCD Minimum Perceptible Color Difference or JNCD Just Noticeable Color Difference, where 1 MPCD = 1 JNCD = Δ(u'v') = 0.0040 on the CIE 1976 Uniform Chromaticity Scale.

Color differences less than 1 JNCD are visually indistinguishable, while values greater than 1 JNCD are visually noticeable when the two colors are touching on-screen. When the colors are not touching and are further apart, the visual threshold for Just Noticing a Color Difference is higher. Here we will use 3 JNCD for the threshold of a visually noticeable display color difference in images. The 3 JNCD color difference is shown in the Figures below.

Display Color Errors less than 3 JNCD on a display are generally not visually noticeable for typical image content and appear accurate to the eye. For an in-depth discussion and analysis of Absolute Color Accuracy see this article.

Color Shifts with Average Picture Level APL
The Colors and Absolute Color Accuracy of the display should not vary as the on-screen image content changes. In a separate Figure 4 we examine and measure the Color Shifts with changing image content from Low APL to 50% APL.

Figure 2b.   sRGB Color Mode Absolute Color Accuracy Plot
The iPhone 13 Pro Max provides a very accurate color match to the sRGB Standard Color Gamut.
The Average Color Error is 0.5 JNCD and the Maximum Color Error is 1.8 JNCD.

Figure 2c.   DCI-P3 Color Mode Absolute Color Accuracy Plot
The iPhone 13 Pro Max provides a very accurate color match to the DCI-P3 Standard Color Gamut.
The Average Color Error is 0.5 JNCD and the Maximum Color Error is 1.9 JNCD.