#
Analyzing All the Instances of a Chaotic Map to Generate Random Numbers^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Chaotic Map

## 3. Analysis of the Map

`0x38e38e38e38e38e3`in hexadecimal, the correlations change, as shown in Figure 3.

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The domain of attraction of the map in Equation (1). This domain was obtained in floating point arithmetic. Moreover, 40,000 points obtained with initial conditions $\left(x\right(0),y(0\left)\right)$=$(-0.5,0.4)$ are shown.

**Figure 2.**In (

**a**) is shown the three correlations between the sequences $({s}_{1},{s}_{2})$, $({s}_{1},{s}_{3})$, and $({s}_{1},{s}_{4})$, and in (

**b**), between sequences $({s}_{5},{s}_{6})$, $({s}_{5},{s}_{7})$, and $({s}_{5},{s}_{8})$.

**Figure 3.**In (

**a**) is shown the three correlations between the sequences $({s}_{1},{s}_{2})$, $({s}_{1},{s}_{3})$, and $({s}_{1},{s}_{4})$, and in (

**b**), between sequences $({s}_{5},{s}_{6})$, $({s}_{5},{s}_{7})$, and $({s}_{5},{s}_{8})$; by now, the value of a in Equation (1) is changed to 1.7777777.

Seq. Name | $\mathit{x}\left(0\right)$ | $\mathit{y}\left(0\right)$ | Code |
---|---|---|---|

${s}_{1}$ | $-0.5$ | $-0.5$ | 00 |

${s}_{2}$ | $-0.5$ | $-0.5+{2}^{-61}$ | 00 |

${s}_{3}$ | $-0.5$ | $-0.5$ | 01 |

${s}_{4}$ | $-0.5$ | $-0.5$ | 02 |

Test Name | Seqs. ${\mathit{s}}_{1}$, ${\mathit{s}}_{2}$, ${\mathit{s}}_{3}$, ${\mathit{s}}_{4}$, ${\mathit{s}}_{5}$, ${\mathit{s}}_{6}$, ${\mathit{s}}_{8}$ | Seqs. ${\mathit{s}}_{7}$ | |
---|---|---|---|

1 | Rabbit | All 40 tests passed | 17/40 |

2 | Alphabit | All 17 tests passed | 1/17 |

3 | Block Alphabit | All 6 repetitions of Alphabit tests passed | 8/102 |

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**MDPI and ACS Style**

de la Fraga, L.G.
Analyzing All the Instances of a Chaotic Map to Generate Random Numbers. *Comput. Sci. Math. Forum* **2022**, *4*, 6.
https://doi.org/10.3390/cmsf2022004006

**AMA Style**

de la Fraga LG.
Analyzing All the Instances of a Chaotic Map to Generate Random Numbers. *Computer Sciences & Mathematics Forum*. 2022; 4(1):6.
https://doi.org/10.3390/cmsf2022004006

**Chicago/Turabian Style**

de la Fraga, Luis Gerardo.
2022. "Analyzing All the Instances of a Chaotic Map to Generate Random Numbers" *Computer Sciences & Mathematics Forum* 4, no. 1: 6.
https://doi.org/10.3390/cmsf2022004006