Predestination and Free Will – The Sierpinski Triangle

Christian theologians have long been vexed by the question of predestination versus free will. The Bible is replete with scripture to support each of these positions. Entire forests have given their lives to the discussion of this topic. I shall not attempt a recap.

The idea of biblical predestination is inescapable. For example, Ephesians 1:11 says
“in him we were also chosen, having been predestined according to the plan of him who works out everything in conformity with the purpose of his will.”
I’m not sure I understand exactly what this means, but the word “predestined” is in there; and in other places in the scripture, both explicitly and by implication.
On the other hand, immediately, at the very foundational decision of the human race, in the second chapter of Genesis (v.16) God says to Adam
16“You are free to eat from any tree in the garden;…”
And much later, in 2 Peter 3 Peter says
The Lord is not …willing that any should perish, but that all should come to repentance.
So which is it? Those who have come to the conclusion that, despite the apparent contradiction, both must be true are probably correct.
The proper topic of discussion here is not “Predestination vs. Free Will” but “Predestination and Free Will”.
The modern mathematical field of chaos theory suggests a way out of the dilemma. The following was discovered using computers; it is strange to the point of astonishing but true. Admittedly this is only a simple example, or analogy for a more complex situation, but I have found it instructive.
Here is an outline of the original discovery in this area. In my analogy, I shall label each step either a decision by God or a free will decision by man.

Sierpinski Triangle after 50,000 iterations (dots)
1. Start with a (large, empty) equilateral triangle – [in the beginning GOD created the equilateral triangle] 2. Pick a point AT RANDOM inside the triangle – [FREE WILL] 3. Pick a corner of the triangle, again AT RANDOM – [MORE FREE WILL] 4. At a point, half-way from the randomly chosen point to the randomly chosen corner, make a dot – [Rules of the System – set by GOD] 5. Repeat from each new dot (50,000 times in this example). The dots form the above triangular pattern. – [it’s “PREDESTINED according to the plan”] 6. Repeat the whole process with a different randomly chosen starting point. You get the same triangle pattern every time! – [PREDESTINATION]

(For a totally clean picture you may have to erase the first few dots.)

Many different predetermined patterns can be generated this way using different starting shapes and different plotting rules.
On human reasoning, the randomly plotted dots would be expected to produce some kind of indeterminate pattern or to evenly fill the triangle. But they don’t. To the best of my knowledge, nobody knows why.
Here we have a mathematical system saturated with free will (random choices) and a predestined outcome (the Sierpinski triangle). Paradoxical, but true.
The person choosing the points has free will but within the system.
Of course, a salvation decision is not a triangle. God’s creation is a far more complex system than we can grasp, and all the rules beyond our understanding (though many leading to success or failure are pointed out in the Bible).

Two scriptures come to mind re this and other seeming Bible “contradictions”.

5 Trust in the LORD with all your heart
and lean not on your own understanding; Proverbs 3:5

9 For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts. Isaiah 55:8-9
Chaos theory opens our minds to new possibilities.