## 2 Materials and Methods
### Practical Application Validation: A Case Study on User Experience Evaluation  
Based on the experimental findings that graphical complexity is modulated by the visual order of internal constituent elements, complexity interference seems to disappear particularly in the process of memory recognition of ordered symbol. To further validate the consistency of the experimental results with user experience in real-world applications, we conducted a design optimization based on a company brand logo (Nanjing Kaishe Zaowu Technology Co., Nanjing, China) The original logo was composed of two intersecting circles and a square, communicating a traditional Chinese business culture of \"TianYuanDiFang, HeQiShengCai\", which means \"a round sky and a square earth, where harmony fosters wealth\". Since the Chinese pronunciation of the circle is \"Yuan\", the two circles in the graphical symbol, respectively, symbolize \"completeness\" (Chinese pronunciation: \"YuanMan\") and \"prospertify\" (Chinese pronunciation: \"YuanBao\"). We optimized the order of the inner elements in the way they are grouped without changing the basic elements (one rectangle and two circles) and the complexity level. Our optimized design was mainly based on our order construction proposed in the experiment, and we have reconstructed the graphical symbol in terms of symmetry, balance, and regularity, which effectively enhances the visual order of the new symbol (as shown in Figure 7). The optimized design retained the symbolism of the original logo while incorporating the infinity symbol, which is more in line with the brand's core values.  
Figure 6: (**a**) Mean accuracy of order as a function of the type of cues paired with words on a given list for the subjects; error bars indicate \(\pm 1\) standard errors. (**b**) Mean reaction time of order as a function of the type of cues paired with words on a given list for the subjects; error bars indicate \(\pm 1\) standard errors.  
Figure 7: A design optimization based on a company brand logo.  
Subsequently, to verify that an ordered graphic design can indeed enhance the visual communication effect and user experience, we conducted a multi-dimensional user experience rating on the original and optimized design based on the User Experience Questionnaire (UEQ) scale. The UEQ is usually used as part of a classic usability test to collect quantitative data about subjects' experiences with a designed object, which is also a standardized questionnaire with 26 questions on a 7-point Likert scale [61]. The questions in the UEQ are organized into 6 subscales to assess attractiveness, dependability, efficiency, novelty, perspicuity, and stimulation in the user experience. In addition, we added an additional three-factor scale: brand attraction, user empathy and subjective complexity on a 5-point Likert scale. Twenty college students, 11 men and 9 women (ages ranging from 22 to 29 years) from Nanjing Forestry University participated in this user experience evaluation. The results are shown in Figures 8 and 9.  
The results of the UEQ scales and the other three scales indicated that there was no significant difference in the complexity scores between the original and optimized symbols, but the optimized ordered graphical symbols had significantly higher-scale results for attractiveness, efficiency, perspicuity, and stimulation, as well as brand attraction and user empathy.