A fractal law is a law that can never be completely obeyed but only approximated.
Let me give some examples of non-fractal laws:
- A speed limit of 25 mph
- Thou shalt not steal
- Do not trespass this property
Now let me give you some examples of fractal-laws:
- Keep your room clean
- Do no work on the Sabbath
- Drive perfectly
- Sin no more
Lets say a mother tells her son to clean up his room. He first sees that the trash can is tipped over and stands it up and puts all the trash back into it. The mother comes and inspects and says his clothes must not be on the floor. He picks up his clothes and stuffs them into his dresser. His mother then inspects and says the floor has not been vacuumed and he needs to fold his clothes in his dresser and put the dirty clothes into the laundry. He complies to all this and his room looks wonderful. His mother inspects and says his bed must be made and the dust on the window sills must be cleaned. Again he conforms but with a bit of frustration and his mother then inspects and hands him a microscope. He looks at the rug with the microscope and sees dust mites constantly pooping on his floor. He then gives up and cries on his bed - he can never obey his mother completely no matter how hard he tries.
A fractal law is not meant to be obeyed completely. It is more like a compass telling us what direction to travel. Unlike a non-fractal law, a fractal law requires constant energy to obey. It requires ACTIVE obedience instead of PASSIVE obedience.
My linefrac program is pretty simple but it can never render any fractal perfectly. It only has so much screen resolution to work with and so can only approximate the fractal. You can zoom into a fractal with my tool over and over and you will never see all of its glorious detail. Some fractals are so complex that the program will take a long time to render even an approximation of it. Some line fractals are "divergent" which means that you can't even render an approximation without purposely giving up at some level of the recursion in order to eventually complete the render.
Conforming our lives to the image of Christ is like that. We can never get there but if we aren't constantly moving toward that target, we are essentially disobeying that fractal law.
In the case of the Christian life, the atonement of Christ frees us from the constant burden of guilt trying to obey fractal laws. We can always find fault with ourselves and we can destroy ourselves trying to meet the demands of a fractal law as we approach the limits of our abilities (or will) to obey it. We may even have to "give up" on obeying some challenging aspect of the law in order to eventually conform to it in some approximate way.
No wonder the word Disciple is based on the word Discipline. To constantly yield ourselves to the image of Christ is to constantly try to become like an infinite fractal.
What adds to the stress are verses like "If your eye offends you, pluck it out...", "He who turns back from his plow is not worthy of me.", "If you teach people to disobey even the least of these commandments, you will be least in the Kingdom of Heaven." and "He who is not for me is against me."
Luckily we have some grace verses like "Lean not on your own understanding but seek first the Kingdom of God and all these things will be added to you.", "He who is not against me is for me." and "He who believes in me shall be saved."
Paul, in Romans 7 devotes an entire chapter to this problem of continuing to sin even though we agree that what we are doing is wrong. His solution is to go schizophrenic and attaches the sin he does to his flesh while attaching his obedience to his spirit. It is the only way for a genuinely devout Christian to maintain his sanity in life.
Obeying in the spirit is something like using limits in math to find the answer to the sum of an infinite series. If you have never studied limits or the Calculus you wont get this but if you have, you can see how a simple formula can describe the infinite series in a way that doesn't require infinite recursion to get the answer.
I wonder if "resting in Christ" and "abiding" with Him is something like applying a limit to the problem of a fractal law. Obeying in the "spirit" to many Christians is simply an attitude of obedience and humility. We just can't get there through works, but by resting in the atonement of Christ we somehow conform to the fractal law perfectly. Our savior magically converts our attitude and gratitude into conformance to a fractal law that can never be obeyed. Christ himself we know lived a perfect life completely free of sin. Even he could not flawlessly obey the Sabbath law but he simply took the attitude of doing what he saw the Father doing. Somehow, even though he admitted on several occasions that he did indeed technically break the Sabbath by doing great works on that day, He claimed perfect compliance to the law because of his attitude during his walk.
Seeing that a law can be a fractal and knowing that we cannot attain to its full obedience EVER is somewhat comforting to me, yet I must continue to strive to conform to that fractal over time or I am really disobeying it. Or... I can chose to "walk in the spirit" at all times. Praying without ceasing to God and seeking his will in every circumstance rather than try to conform to fractal laws with more and more precision as I grow. One way gives constant guilt and stress while the other gives peace and rest.
So let's "take it to the limit" and walk with Christ each day as our friend and example and leave the infinite recursion to Him to complete for us.