Fractals— never heard of them until this fall. Fractal is a comparatively new term coined in 1975 by Benoit Mandelbrot. It’s from Latin meaning broken or fractured. We’ve always seen fractals, we just didn’t use that term. God used fractals in Creation. Let’s see how they are used in our Christmas celebrations.

Fractals are patterns. Nature is filled with patterns. Our Christmas trees are fractals. From the trunk we have limbs, then branches, then needles. Depending on the type of evergreen, the needles may be flat or in whorls. these are all patterns of the trunk. Fractals are replicas of a larger item that becomes smaller with each replication. The tree is confined to its full-grown size yet it continues to repeat its pattern smaller and smaller during the life of the tree.

Have you seen snowflakes under a microscope? They too have a shape that is repeated many times but becomes smaller with each replication. You may have tried to draw a Koch snowflake beginning with a triangle. The size of the triangle determines the size of the snowflake. More triangles can be added to the shape but none can be larger than the original area.

Many fractals are in the form of spirals. Pinecones, curly hair, poinsettia petals are all spirals. (Actually, poinsettia petals are leaves that are replicas of the stem. Notice how the veins branch out like the stems) Even our universe that held the Bethlehem Star was created in a spiral.

We are fractals too, broken and fractured, repeating ourselves with each generation. However, Jesus was not a fractal of His earthly parents because only Mary was His earthly mother. Boys usually look and act a lot like their dads. Jesus told his disciples if you have seen me, you have seen the Father. Jesus acted like His Father. Jesus, God’s only Son, is God in the flesh, without sin. We celebrate the One who came to do what we in our limited abilities cannot do. We cannot live sinless lives and we cannot do enough good to save ourselves. However, we can receive the gift that Jesus came to give, the gift of eternal life given to all who choose to receive it.

When we receive the gift of eternal life we become a fractal of Jesus. We are reborn in His image. He is the vine and we are the branches. When we are broken and made in His image then and only then will the earth be filled with the knowledge of the Lord. This Christmas may we all be fractals of the Branch.

 And there shall come forth a rod out of the stem of Jesse, and a Branch shall grow out of his roots:

They shall not hurt nor destroy in all my holy mountain: for the earth shall be full of the knowledge of the Lord, as the waters cover the sea.

And in that day there shall be a root of Jesse, which shall stand for an ensign of the people; to it shall the Gentiles seek: and his rest shall be glorious. Isaiah 11:1,9-10

https://www.cs.mcgill.ca/~rwest/wikispeedia/wpcd/wp/f/Fractal.htm https://www.crayola.com/lesson-plans/fractal-facts-lesson-plan/ https://www.scienceworld.ca/stories/patterns-nature-finding-fractals/

Blessings, Gail Cartee