Christophe LETELLIER
08/12/2023

Denise Sciamarella and Gabriel Mindlin designed the four-dimensional system [1]

from a three-dimensional system proposed by Deng [2] For appropriate parameter values as

this system produces a chaotic attractor (Fig. 1). A solution to this system was investigated with a cell complex in their work. It was recently revisited in terms of templex [3]

**Fig. 1. Chaotic attractor produced by the four-dimensional system.**

From the complex of cells Here, a templex was built and, then, a template constructed as drawn in Fig. 2.

**Fig. 2. A direct template for the four-dimensional attractor.**

[1] **D. Sciamarella & G. B. Mindlin**, Unveiling the topological structure of chaotic flows from data, *Physical Review E*, **64**, 036209, 2001.

[2] **B. Deng**, Constructing homoclinic orbits and chaotic attractors, *International Journal of Bifurcation & Chaos*, **4**, 823-841, 1994.

[3] **G. D. Charó, C. Letellier & D. Sciamarella**, Templex : A bridge between homologies and templates for chaotic attractors, *Chaos*, **32** (8), 083108, 2022. Online