# The Reappearance of Poetic Beauty in Chaos

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## Abstract

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## 1. Introduction

## 2. Formal Beauty in Chaos

## 3. Beauty of Symmetry

## 4. Asymmetrical Beauty in Chaos

## 5. Extending Beauty

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**“Lonely smoke straight in the desert, the long river of the yen down” by poet Wei Wang (Tang Dynasty).

**Figure 2.**Typical smoke-like dynamical behavior: (

**a**) x-y plane, when a = 0.6, b = 3, IC (initial conditions) = (1, −1, 1) in System (1), (

**b**) basins of attraction in System (2) for coexisting reflection symmetric attractors in the y = −1.5.

**Figure 3.**Typical coexisting goose-like attractors: (

**a**) x-z plane, where a = 3 in System (3) and upside: IC = (0, −0.23, 1), underside: IC = (0, 0.23, −1), (

**b**) when a = 3.55 and b = 0.5 in System (4), the initial conditions from left to right are respectively set to: IC = (−5, 0, −1), IC = (−2, 0, −1), IC = (−1, 0, −1), and IC = (2, 0, −1).

**Figure 4.**Typical butterfly-like attractors: (

**a**) x−z plane, when a = 10, b = 8/3, and c = 28, IC = (1, 1, 1) in System (5), (

**b**) x−z plane, when a = 0.6, b = 1, c = 1, d = 4, and e = 2, IC = (1, 1, 1) in System (6).

**Figure 5.**Typical coexisting fish-like attractors of Systems (7) and (8): (

**a**) x−z plane, when a = 0.4, b = 1.75, c = 3, and d = 6.2 in System (7), the initial conditions from left to right are, respectively, set to: IC = (1 − π, −1, 1), IC = (1, −1, 1), IC = (1 + π, −1, 1), and IC = (1 + 2π, −1, 1), (

**b**) when a = 1.22, b = 8.48, d

_{1}= 2, d

_{3}= 2.2, and d

_{4}= 0.45 in System (8), left side: IC = (−1.5, 3.2, 0.95) and right side: IC = (1.5, 3.2, 0.95).

**Figure 6.**Typical conch-like attractors: (

**a**) when a = 1.99 and IC = (0.1, 0.1) in map (9), (

**b**) coexisting phase orbits of System (10) on x-z plane, where a = 1.2 and b = 1.2, left side: IC = (−2, 0, 3), right side: IC = (2, 0, 3).

**Figure 7.**Typical fan-like attractors: (

**a**) coexisting attractors of System (11) on y-z plane, where right side: IC = (0, 0.1, 0) and left side: IC = (0, –0.1, 0), (

**b**) coexisting orbits of System (12) on x-z plane, where upside: IC = (1, 1, 1, 1) and downside: IC = (–1, –1, –1, 1).

**Figure 8.**Typical asymmetrical attractors: (

**a**) x-y plane, when a = 6 and b = 1 under IC = (1, 1, 0) in System (13), (

**b**) x-y plane, when a = 0.9 and b = 1 under IC = (0.8, −2, 0) in System (14).

**Figure 9.**Typical extending attractors: (

**a**) y-z plane, when a = b = 0.2 and c = 5.7 under IC = (−9, 0, 0) in System (15), (

**b**) y-z plane, when a = 0.2, b = 0.2, and c = 6.5 under IC = (1, 0, 1) in System (16).

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**MDPI and ACS Style**

Sheng, S.; Wen, H.; Xie, G.; Li, Y.
The Reappearance of Poetic Beauty in Chaos. *Symmetry* **2022**, *14*, 2445.
https://doi.org/10.3390/sym14112445

**AMA Style**

Sheng S, Wen H, Xie G, Li Y.
The Reappearance of Poetic Beauty in Chaos. *Symmetry*. 2022; 14(11):2445.
https://doi.org/10.3390/sym14112445

**Chicago/Turabian Style**

Sheng, Suqiao, Huiyu Wen, Guangfu Xie, and Yongxin Li.
2022. "The Reappearance of Poetic Beauty in Chaos" *Symmetry* 14, no. 11: 2445.
https://doi.org/10.3390/sym14112445