## 3 Results and Discussion
### Gamut Exploration
In the process of color gamut exploration, because the new marking samples are obtained through genetic algorithms, it is possible that there will be two adjacent generations of the color gamut for the same situation, i.e., that a new generation of marking samples will not appear outside the color gamut of the color parameter; repetitive marking was used to avoid this possibility. In addition, it was found that the optimal parameter combinations selected in each generation corresponded to the four different hues of colors in the CIE 1931 color  
Figure 4: The most representative genetic algorithm results based on color gamut maximization prediction. (**a–f**) represent the results of laser-induced coloring in the first, fifth, tenth, fifteenth, seventeenth, and twentieth generations, respectively. Among them, the 17 th generation reaches convergence, and the 20 th generation is a verification of whether it is locally convergent. (**g–l**) correspond to the color gamut maximization prediction results of the first generation, fifth generation, tenth generation, fifteenth generation, seventeenth generation, and twentieth generation laser induced coloring samples, respectively; (**m**) displays the selection criteria for the optimal parameter combination, taking the 15 th generation as an example; (**n**) shows the position of the optimal parameter combination in the hue wheel in the 15 th generation. coordinates; these four different hues were mapped to the hue wheel and were found to be in four different quadrants, as shown in Figure 4n. It was assumed that each optimal color gamut combination was represented by a color weight \(q\). Only when a parameter combination with a higher color weight \(q\) appeared would the maximum color gamut of the population increase. Otherwise, the maximum color gamut would remain unchanged. The color weights were calculated as follows:  
\[q=\sqrt{a^{2}+b^{2}} \tag{12}\]  
\(q\) represents the weight of the color parameter and is related to the color parameters \(a\) and \(b\). There are four color weights \(q\) for each population, and \(q\) is only compared with the color weights of the previous generation that are in the same quadrant of the hue wheel with the same signs of the color parameters \(a\) and \(b\). As \(q\) increases, the color weight becomes larger, and the color is more likely to be selected as the optimal color to represent the chromatic gamut. Relevant studies have indicated that scanning speed is positively correlated with color brightness and hue, while laser energy and scanning spacing exhibit a negative correlation with color hue and brightness, respectively. Additionally, laser frequency is negatively correlated with brightness [31]. This demonstrates that the formation of structural colors involves multiple factors interacting with each other, and we explored the relationship between parameter combinations and color gamut changes as a whole. We compared color parameter samples spanning from the first to the seventeenth generation. In the initial population of the first generation, due to the matrix distribution of laser parameters, parameters having positive and negative correlations with color constrained each other, leading to a small initial maximum color gamut of merely 0.00048. As the population grew, excellent laser parameters were preserved in each generation and contributed to the generation of new parameter combinations. Parameters such as scanning speed, laser power, laser frequency, and scanning interval gradually attained optimal values for color and combined with each other, thereby inducing high brightness, high saturation, and various hues of colors. Consequently, the color gamut continuously expands, reaching 0.0022 in the 17 th generation. During the iterative process, emerging excellent parameters induced rich colors, with these colors exhibiting larger \(a\) and \(b\) values and color weights.