As science was trying to understand the dynamics of complex systems (Chaotic Systems) in nature such as a waterfall or the weather, science discovered the seemingly infinite dimensions of nature. Here we see the modeling of Edward Lorenz strange attractor. He came across loops of spirals infinitely deep never joining or intersecting within a definite space. How could infinitely many paths lie in a finite space? The reason why they never intersect is because they lie on different planes. Another insight came when it was realized that there was scaling in nature, that is, the same basic patterns on smaller and smaller scale was deeply embedded in natural forms. Note below an enlarged smaller section of the Mandelbrot set.
Likewise, in studying the edges of the Mandelbrot James Gleick wrote, "The boundaries is where points are slowest to escape the pull of the set. It is as if they they are balanced between competing attractors, one at zero and another, in effect ringing the set, at a distance of infinity." 89
Meaning of Infinity?
Usually we think of infinity as something without end. This is not the meaning of Infinity in its ultimate sense. Only God can be considered Infinite in his essence meaning not finite, not a creature, but creatures may be said to flow infinitely from the Creator. In attractors the mathematicians speak of infinitely long orbits or repeated scaling within a definite space. What could this possibly mean? St. Thomas states, "A potentially infinite multitude is possible, because the increase of multitude follows upon division of the magnitude, since the more a thing is divided, the greater the number of things result." (Summa Q. 7, Art. 4) But this division by the Strange Attractors is due to scaling, that is self-similitude being created at ever smaller dimensions of magnitude within a reality. The comment by James Gleick suggests to me that although computer creatures are finite, they exhibit the presence and pull of the Infinite (not finite) presence in order to come into being. So the apparent "infinity" produced by the strange attractors is ultimately the work of the infinite God. God's infinity is reflected by the creature as an unending process, but the creature in itself is not infinite, as God is Infinite.
For what it may we worth in this perspective, the 0 in mathematics originated in India and was derived from the primordial sound OM (AUM), origin of all other sounds and meaning the Void or supreme reality which we call God. Zero than in mathematics may be considered the nothingness and origin of all numbers.
St. Thomas Aquinas asks, "Does God know infinite things?" By infinite he means the countless things produced by God. He answers that since God knows the actual and possible known to Himself and created things which presumably are without end, God knows infinite things. We know that generations will end but God knows the thoughts the affections of hearts of intelligent creatures will have no end, so God knows infinite things. (Summa, Q. 14, Art. 12)
Great is our Lord,
and of great power:
his understanding is infinite."
God the Chaos Attractor