Three-dimensional (3D) genome organization plays a critical role in gene expression regulation and function. Recent advances in Hi-C and Micro-C data across various species provide insights into the mechanisms governing 3D genome formation, such as loop extrusion. While visual patterns like topologically associating domains (TADs) and loops are conserved across species, the underlying biological mechanisms may differ. Both species-specific architectural factors and DNA sequences influence chromatin folding, complicating comparative studies on the evolution of 3D organization of the genome. This work leverages existing Hi-C data and machine learning to explore species-specific 3D genome folding mechanisms and predict chromatin structures from DNA sequences. Here, we present Chimaera (convolutional neural network for Hi-C maps prediction using autoencoder for maps representation), a neural network that not only predicts Hi-C maps from DNA sequence, but also enables the search, quantification, and interpretation of associations between DNA sequences and 3D genome patterns. Firstly, we demonstrate that Chimaera predicts Hi-C or Micro-C contact maps from DNA sequences, enabling the interpretation and extraction of key biological mechanisms. By exploring the latent representations generated by Chimaera, we offer a tool for building an unsupervised atlas of chromatin features such as insulation, loops, stripes, and fountains/jets. We demonstrate the capabilities of Chimaera by detecting and quantifying signatures of insulation and fountains in Hi-C data, applying it to well-characterized biological processes like the cell cycle and embryogenesis. Additionally, we perform a targeted search for DNA sequence elements associated with specific chromatin structures, advancing our understanding of genome organization. By extending the search of DNA sequence elements to multiple species, we confirm the role of CTCF in generating insulation patterns in vertebrates and BEAF-32 in Drosophila, and identify motifs previously not reported in mouse and Drosophila. In Dictyostelium, Chimaera demonstrates the importance of gene arrangement on the DNA strand for the formation of loops, confirming the hypothesis about the impact of convergent gene positioning on 3D genome organization in this amoeba. A pronounced but diverse effect of genes is evident when predicting chromatin interactions in other organisms. Finally, we train the model on data from one species and then apply it to cross-predict how the genomes of other organisms might fold within the cellular environment of the original species. We thereby test whether chromatin folding patterns are transferable between species and reveal evolutionary similarities across genomes by building a chromatin-based cluster tree of species ranging from plants to mammals.