Mandelbrot: A Mathematical Equivalent to “Express Likeness of His Father”

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Each of these crowns consists of similar "seahorse tails"; their number increases with powers of 2, a typical phenomenon in the environment of satellites. Created by Wolfgang Beyer with the program Ultra Fractal 3.

The Doctrine and Covenants teaches that Seth “was in the express likeness of his father, insomuch that he seemed to be like unto his father in all things….” I used to read this as Seth and Adam simply looked alike.

As I’ve gotten older and have started looking more like my parents, I realized the scripture says that Seth “seemed to be like unto his father in all things.”  All things—like idiosyncrasies, habits, thought processes, decision making, righteousness. Seth being like Adam in all things implies similarities in much more than just looks.

Paul, in teaching that God the Father spoke to man through prophets and then His Son, specifically mentioned that Jesus was exactly like His Father “being the brightness of his glory, and the express image of his person.”

During the Savior’s last mortal Passover, when Phillip asked Jesus to show them the Father,

Jesus saith unto him, Have I been so long time with you, and yet hast thou not known me, Philip? he that hath seen me hath seen the Father; and how sayest thou then, Shew us the Father?

Believest thou not that I am in the Father, and the Father in me? the words that I speak unto you I speak not of myself: but the Father that dwelleth in me, he doeth the works.

Believe me that I am in the Father, and the Father in me: or else believe me for the very works’ sake.

I was taught, and believe, that God the Father and Jesus Christ are two separate and distinct persons. But though physically separate persons, Heavenly Father and Jesus work unitedly in purpose and vision. Thus, They are one.

My rational mind wasn’t satisfied. I always felt there was a deeper answer,  something more, something I hadn’t comprehended yet. Verses like Doctrine and Covenants 88:41 demanded more contemplation than just believing the hand of God creating everything with some portion of Him strategically planted inside.

He comprehendeth all things, and all things are before him, and all things are round about him; and he is above all things, and in all things, and is through all things, and is round about all things; and all things are by him, and of him, even God, forever and ever.

I comprehend truth visually. I digest knowledge in my mind aided by intuitive forces. And when I think I’ve reached an understanding and found truth, I seek confirmation in my heart. Mind and heart, my two internal witnesses of truth. But I could not visually comprehend these consistently profound statements.

How is it done? How is it physically possible? I could not see it.

Mandelbrot Sets

Then I learned about Mandelbrot sets.

Original Mandelbrot set
Initial image of a Mandelbrot set zoom sequence with a continuously colored environment

Simply stated, a Mandelbrot set includes complex numbers that do not diverge in a specific mathematical function and remain bounded in absolute value. So to create images, complex numbers are sampled and determine if the iteration of the function goes to infinity.  Colors identify how rapidly points diverge or don’t diverge.

Mandelbrot sets show self-similarity, meaning that as you zoom in from the original image to its smaller units, you find the original image repeated over and over infinitely. So the smallest structure replicates the largest, the only differential based on the iteration’s size.

So, the smallest iteration is the express likeness of the first iteration, the original.

Here’s a sample of a zoom starting from an original point and zooming straight down on the figure to 750,000,000 iterations, picking up the pattern’s obvious repetitions over and over again. Notice how each iteration is an exact, though smaller, representation of the original. As the zoom intensifies, you can’t even really tell that the iteration is exponentially smaller than the original. Time and relative perspective equalize the view.

Behold, I am from above, and my power lieth beneath. I am over all, and in all, and through all, and search all things, and the day cometh that all things shall be subject unto me.


And the Lord God spake unto Moses, saying: The heavens, they are many, and they cannot be numbered unto man; but they are numbered unto me, for they are mine.

And as one earth shall pass away, and the heavens thereof even so shall another come; and there is no end to my works, neither to my words. For behold, this is my work and my glory—to bring to pass the immortality and eternal life of man.

Here is a still shot of a large iteration encircled by smaller versions of itself.
Mandelbrot set rendered using a combination of cross and point shaped orbit traps. Created by wiki user Simpsons_contributor

Iterations of Clarity

Math enabled me to visualize the truths that my limited understand obscured.  I could see how something could be “through and in” because of the way it connects to creation.

I could see iterations with agency (people) “attaching” to the original through covenant and ordinance, taking on the Original’s Name and characteristics, learning His mind and will, acting in His name, becoming one with Him.

Mandelbrot seahorse valley
Partial view of the Mandelbrot set. Step 9 of a zoom sequence: The “seahorse valley” of the satellite. Magnification relative to the initial image: 4,647,300 Created by wiki user SimsContPics

At Atonement’s door, the Savior prayed to the Father.

And for their sakes I sanctify myself, that they also might be sanctified through the truth….

That they all may be one; as thou, Father, art in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me.

And the glory which thou gavest me I have given them; that they may be one, even as we are one:

I in them, and thou in me, that they may be made perfect in one;

Made perfect in one by becoming the express likeness of our Savior and Father.