The Simple Explanation suggests that a "universal unit of consciousness" carries all of the information that manifests as our particular time/space continuum. This universal unit of consciousness is the primal algorithm of the set of laws that govern our universe. Some people call that God. Other people think it all can be boiled down to math and physics.
The National Geographic article calls Gaudi's approach "biomimetic architecture."
Here's a quote from the National Geographic article:
"As idiosyncratic as Gaudí himself, it is a vision inspired by the architect's religious faith and love of nature. He understood that the natural world is rife with curved forms, not straight lines. And he noticed that natural construction tends to favor sinewy materials such as wood, muscle, and tendon. With these organic models in mind, Gaudí based his buildings on a simple premise: If nature is the work of God, and if architectural forms are derived from nature, then the best way to honor God is to design buildings based on his work. As the Barcelona scholar Joan Bassegoda Nonell notes, "Gaudí's famous phrase, 'originality is returning to the origin,' means that the origin of all things is nature, created by God." Gaudí's faith was his own. But his belief in the beautiful efficiency of natural engineering clearly anticipated the modern science of biomimetics."
Yes, toroidal forces appear is in this cathedral in many forms. Here's what Wikipedia says about the hyperboloids:
"Gaudí used hyperboloid structures in later designs of the Sagrada Família (more obviously after 1914), however there are a few places on the nativity façade—a design not equated with Gaudí's ruled-surface design, where the hyperboloid crops up. For example, all around the scene with the pelican there are numerous examples (including the basket held by one of the figures). There is a hyperboloid adding structural stability to the cypress tree (by connecting it to the bridge). And finally, the "bishop's mitre" spires are capped with hyperboloid structures. In his later designs, ruled surfaces are prominent in the nave's vaults and windows and the surfaces of the Passion facade."
Here's an image of a hyperboloid
Do you see that this mathematical structure is also the central funnel of the torus? The hyperboloid shape can have a wide waist or a narrow waist.
Natural light is funneled through the cathedral's ceiling through numerous hyperboloidal skylights. Hyperboloid skylights allow more light to enter because light rays follow the same straight lines that create the circular cut-out. Take a look at the image of the hyperboloid above. Do you see how the grid lines that seem to swirl around are actually straight? A ray of light that enters along one of the grid lines at the top of the figure goes straight along wall of the hyperboloid through the middle to an apparently wider diameter than the size of the hole. A simple hole or tube only allows the light to go straight down the sides of the cut-out.
The twisting of the columns also follows the hyperboloid which provides structural strength. A hyperboloid column distributes load more efficiently than a traditional straight column.