Righteous Fractals Topology of Human Hodological Spaces: Forming an Archetype Picture of Christ Jesus

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. — John von Neumann¹

The son of a Christian minister, Félix Émile Borel published Sur quelques points de la théorie des fonctions ("On some points in the theory of functions"), in 1893. He pioneered measure theory and probability. Benoit Mandelbrot later stated that "a fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." The Mandelbrot set arises from a simple function equation, 𝑓c (z) = z² + c. Shape1

z → z² + c
z → z² + 1 z always starts as 0.
0 → 0² + 1 the result is 1.
After calculating a first result, that result (1) is used as the new value for z.
1 → 1² + 1 result is 2, so for the next calculation or iteration, 2 for z.
2 → 2² + 1 result is 5 for the next iteration.
5 → 5² + 1 result is 26 etc.

The result of Mandelbrot’s formula is that for c = 1, it goes towards infinity. All points that never go to infinity are part of the Mandelbrot set.

z → z² – 1
0 → 0² - 1 result is -1, so -1 for z in the next iteration.
-1 → -1² - 1 result is 0, so z = 0 for the 3d iteration.
0 → 0² - 1 result is -1 again, using z = -1 for the 4th iteration.
-1→ -1² – 1
0 → 0² – 1
-1 → -1² - 1 etc.
So for c = -1 Mandelbrot’s formula doesn’t grow to infinity but oscillates between -1 and 0.

For making a simple picture on a computer, only use the horizontal x-axis. For the vertical y-axis, understanding imaginary numbers is a prerequisite. The iterations are the number of repetitions needed to find out if a starting value goes to infinity. As soon as the result of a iteration is larger than 2, stop calculating because all results over 2 will always go towards infinity and can never be a part of the Mandelbrot set. For c = 1 the iteration-chain looks as also seen above:
For the first iteration 0 → 0² + 1
The second iteration 1 → 1² + 1 result is 2
The third iteration 2 → 2² + 1 result is 5 etc.
With the second iteration, it’s clear that the result will inevitably become larger until infinity. So calculating stops and the next pixel is calculated.

The white points, the fractal boundaries, are the values of c for which 0 diverges to infinity and the black is the values of c for which 0 stays confined. On the edge of the Mandelbrot set, where the white and black parts of the plane meet, the edge exhibits self-similarity and also hides an endless sea of complexity. Because there exists an infinite number of points between two points along the number plane the Mandelbrot set’s detail is considered to be infinite. Fractals’ similar nature means, no matter the magnification, patterns keep reappearing, especially in Mandelbrot sets.³ See color figure (2) below.⁴

The geometric patterns of snowflakes are also seen in fractal laser light, as in image (3) below.⁵

Beyond what looks to be a smeared mass of light, with precise control of laser light within a laser’s spherical mirrors, light gets to a smaller or larger version of itself every time it returns to a point where it could be observed – resulting in fractals.⁶

In an email exchange with Dallas F. Bell Jr. in May, 2021, co-discoverer of fractal laser light, Johannes Courtial, physics professor at the University of Glasgow, indicated that there is an algorithm that can create the patterns of fractal light in a laser,⁷ and there are algorithms for evaluating the fractal dimension of patterns.⁸ Co-discoverer of fractal laser light, Andrew Forbes, physics professor at the University of Witwatersrand (Wits), explained to Dallas F. Bell Jr. in an email exchange in May, 2021, that he calculated the structures by iterating the loop in the cavity many times.

Augustin-Jean Fresnel understood light is a transverse wave. His equations are complex, which means they consider both the magnitude and the phase. They correctly predicted the direction of polarization of the reflected beam when the incident beam was polarized at 45° to the plane of incidence.

The crooked shall be made straight.⁹ The elect have straight paths (Greek hodos).¹⁰ The non-elect have crooked paths.¹¹ Jesus had a perfectly straight/righteous path.¹² Manually calculating His infinitely perfect life would take years to form a finite picture. The perturbations, of adherence and timing etc., from the mapping¹³ of Jesus’ perfection, including the underlying commandments,¹⁴ by finite humans will form unique fractal patterns known to infinite God.

Jesus modeled the righteous path humans are to liturgically follow. The fractal behaviors of His commandments are represented below, with indexed numbers. They are positive in that they finitely (in time and space¹⁵) reflect what He did and not what He did not do, which is implied. For example, He did not use reverse psychology (deceit) to manipulate the behavior of others.

Christ¹⁶ (Son of God) ∞ → BEGIN (Jesus biology) c. 6 B.C.:
1) Asked and answered academic questions,¹⁷
2) Had discipline,
3) Went about His Father’s business,¹⁸
4) Increased in wisdom,
5) Increased in stature,
6) Increased in favor with God,
7) Increased in favor with man,¹⁹
8) In obedience was baptized,²⁰
9) Was patient,²¹
10) Fasted,²²
11) Resisted Satan,²³
12) Quoted Scripture,
13) Taught Scripture,²⁴
14) Built an organization,²⁵
15) Blessed the poor,²⁶
16) Had a pure heart,²⁷
17) Healed the sick,²⁸
18) Brought souls to the truth of salvation,²⁹
19) Loved enemies,³⁰
20) Was efficient,
21) Was thankful,³¹
22) Was frugal,³²
23) Promoted equality for women,
24) Promoted equality for all people,³³
25) Was secure,³⁴
26) Endured slander,³⁵
27) Blessed children,³⁶
28) Was humble,³⁷
29) Managed people,³⁸
30) Taught principles,³⁹
31) Had an eternal perspective,⁴⁰
32) Had righteous anger when the Father was not respected,⁴¹
33) Was just,⁴²
34) Loved the Father with all His heart and mind,⁴³
35) Loved His neighbor as Himself,⁴⁴
36) Had Divine timing,⁴⁵
37) Wept over others,⁴⁶
38) Was honest,⁴⁷
39) Never attributed the work of the Holy Spirit to Satan,⁴⁸
40) Defied a government leader,⁴⁹
41) Endured conspiracies,⁵⁰
42) Enjoined the singing of hymns,⁵¹
43) Demonstrated diplomacy,⁵²
44) Endured torture,⁵³
45) Prayed to the Father,⁵⁴
46) Demonstrated mercy,⁵⁵
47) Did not defend Himself,⁵⁶
48) Took care of friends and family,⁵⁷
49) Forgave others,⁵⁸
50) Wept over Jerusalem,⁵⁹
51) Rebuked hypocrites,⁶⁰
52) Encouraged others,⁶¹
53) Submitted to the Father’s will,⁶²
54) Endured stress,⁶³
55) Called no man Father,⁶⁴
56) Served others,⁶⁵
57) Forgave His murderers,⁶⁶
58) Died for others,⁶⁷
59) Was courageous,⁶⁸
60) Ignored religious and government leaders,⁶⁹

END Christ Jesus (biology) c. 30 A.D. → BEGIN Christ Jesus (resurrected body) ∞⁷⁰

Man is made in the rational image of God.⁷¹ Not doing what God demands and Jesus modeled is sin against His immutable Being. Hamartiology (Greek hamartia meaning a sin) is the study of sin. It deals with the origin of sin, its affects, and its results, especially after death. The daughter of a British Christian minister, Jane Austen’s writings reflected her Christian beliefs. The characters in her seven novels often demonstrated Jesus’ life liturgies and the power of His virtues, such as humility and reason etc. Another daughter of a British Christian minister, Emily Brontë’s (pseudonym Ellis Bell, 1847) single novel, Wuthering Heights, tells of Catherine and Heathcliff’s adulterous thoughts toward each other and the consequences of sin, including depression and an early death. Brontë’s Catherine and another character, Isabella, may be compared to Austen’s Catherine and Isabella in her Northanger Abbey (1818).⁷² Austen’s style depicted general Christian virtues as did the Russian Christian Lev (Leo) Tolstoy. His (1878) Anna Karenina explored Anna’s adulterous behavior with Count Vronsky and her self-initiated death, the ultimate consequence of sin, much like Brontë. It can be argued that Bronte’s style has more introspection of specific Christian values⁷³ than Austen and Tolstoy, much like the Russian Christian Fyodor Dostoevsky, especially in his (1873) Demons.⁷⁴ Paul’s actual discourse before King Agrippa’s court (Acts 26) can be compared to William Shakespeare’s fictional speech by Polonius before the king and queen in Hamlett (Act 2, Scene 2, 86-95).⁷⁵ Paul’s goal is to use his intellect to reflect Jesus’ autotelic virtue, i.e. humility etc., while Polonius demonstrates the art of rhetoric for rhetoric’s sake—l'art pour l'art.

Many attacks on God are strategically more direct. They are generally aimed at discrediting God’s immutable Scripture. For example, an intentional misinterpretation of the passage “the Word was made flesh and dwelt among us”⁷⁶ is often cited as “Jesus or the Scriptures became corrupted etc.” to accommodate non sola Scriptura believers (violators of Jesus’ model 12 and 13). Clearly the passage means Christ came to earth as Jesus who died for the redemption of mankind’s sin.⁷⁷ An old tactic is to promote Jesus not dying and being resurrected for man’s sins, as the Scripture teach, and having been buried elsewhere, such as Kashmir, India⁷⁸ (violation of Jesus’ model 58). The latest heresy is that Jesus Scriptural account of His prophesied biological virgin birth is a description of Him being a female clone of Mary, having XX chromosomes, and not being male with XY chromosomes⁷⁹ (violating Jesus’ model 38 etc.). It is foolish for finite beings to oppose infinite God. Operating on The Greater Fool Theory,⁸⁰ fools believe they can sell their bankrupt anti-Christ ideas to people that are even greater fools than they are.

As with Jesus, the non-elect’s attack strategy on God’s elect is to physically murder them or certainly incapacitate them. Their mental health and motives are to be mocked.⁸¹ They, their families, and supporters are to be threatened and slandered. Jobs, food, and shelter are to be denied. Finances are to be depleted. They are to be opposed in civil and criminal courts. Paul noted that He that called the elect did not cause the elect to disobey the truth. It was a little leaven that leavened the whole lump.⁸² The fractals or fruits of the flesh range from adulteries to heresies and murders,⁸³ while the fractals or fruits of the Spirit range from love to peace and faith.⁸⁴ Those that are Christ’s elect have crucified the flesh and walk in the Spirit.⁸⁵ They expect trials⁸⁶ and know they are conquerors.⁸⁷ They defeat the non-elect’s disproportionate force, who know their time is short, with accomplishing their Divine calling and being happy.

The Divine tavnith (Hebrew for pattern) is seen the tails of figure 1 and 2 presented earlier. The tail of the Mandelbrot set is a baby or smaller version of the parent version itself. Those shapes have existed since creation since numbers can not change. That prevents accounting for fractals with evolutionary theory. Unlike mathematical fractals, physical fractals, i.e. DNA etc., are made of atoms and do not repeat forever.

Knowledge involves coded overlap or fractals of data, as seen with this paper and other papers regarding systematic political science. The wise find out the knowledge of witty inventions⁸⁸ and lay up knowledge.⁸⁹ The seven day process found in the biblical creation of the physical dimension in Genesis 1 is symbolically repeated in the making of the human intellectual dimension in Genesis 1 and 2, and the human moral dimension in Genesis 2 and 3. The elect understands the Genesis 1 account so they can understand the Genesis 2 account and then the Genesis 3 account and vice versa. This makes the rest of the Bible fractal patterns understandable for the elect and not understandable to the non-elect. Mathematically, it is obvious that sola Scriptura, the inspired words of God (see endnote 24), allows for the potential understanding of God’s revelation(s) while non-belief, sadly, prevents it causing blindness and vulnerability to all damnable fractal heresies.

The first fractal heresy by Satan to mankind was what God says is not true.⁹⁰ When accepted by humans, as with Eve, this is idolatry in that Satan, the father of lies,⁹¹ becomes a god.⁹² Whoever is considered to be the authority for truth, instead of Christ Jesus,⁹³ is a god. As a liar, Satan is also a thief because he steals lives as a murderer.⁹⁴

The 2018 International Organization for Standardization (ISO) 31000 provides principles and guidelines for managing risk. It defined risk as the effect of uncertainty on objectives. Risk management is often defined as the identification, evaluation, and prioritization of risks. This is followed by a coordinated application of resources to minimize, monitor, and control the probability or impact of negative events or to maximize the positive opportunities.⁹⁵

The hodological spaces of human behavior may seem to be a chaotic set of experiences, individually m’dor l’dor.⁹⁶ However their topology shows they are variables of a common risk pattern.⁹⁷ That fractal risk pattern is either positive eternal existence with Christ Jesus or negative eternal existence without Him. By His perfect model, it is obvious that finite humans can not measure up—tunnel junction⁹⁸ hamartiology. Eternal risk management involves the adherence to Scripture. They say that only by man’s submission by faith can man truly be redeemed. Thus, the effect of uncertainty on the objective of going to heaven is no longer risky.

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work. — John von Neumann⁹⁹

1 The quote is taken from a speech to the (1947) national meeting of the Association for Computing Machinery, as quoted in Franz Alt’s Archaeology of computers: Reminiscences, 1945-1947. Neumann reasoned at the end of his life that the Christian Pascal was right. Neumann said, “There probably is a God. Many things are easier to explain if there is than if there isn't.” (John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence and Much More, 1992, by Norman Macrae, p. 379.)

15 Zonglu He’s, professor of economics at Kaetsu University, (2018) Integer-dimensional fractals of nonlinear dynamics, control mechanisms, and physical implications determined that “If fractals model complex physical processes and dynamical systems, the nonlinear dynamics and the control physical laws for these fractal-dimension physical processes should result from fractal-dimension spacetimes. Alternatively, fractals may occur in integer-dimension spacetimes.”

73 Thanks is extended to Jay Clayton, professor of English and director of the Curb Center for art, enterprise, and public policy at Vanderbilt University, for his email exchange with Dallas F. Bell Jr. during May, 2021.

Christian references list in Emily Brontë, Wuthering Heights, Barnes and Noble Inc., (2004) New York:

p. 7, “possessed swine,” Luke 8:30; p. 21, “helmet of salvation,” Eph. 6:17; p.21, “broad way,” Matt. 7:13-14; p.23, “seventy times seven,” “seventy-first,” Matt. 18:21-22; p. 24, “know him no more,” Job 7:10; p. 24, “thou art the man,” II Sam. 12:7; p. 24, “judgment,” Ps. 149:9; p. 24, “every man’s hand,” Gen. 16:12; p. 83, “Noah and Lot,” II Peter 2:5, 7; p. 83, “Jonah,” Jonah; p. 102, “broad road,” Matt. 7:13-14; p. 111, “if you fancy,” Satan, “study of revenge,” in British Christian John Milton’s Paradise Lost, Book 1, Arcturus Publishing (2017), London, p. 12; p. 123, “an exile,” Moloch, “what can be worse,” in Paradise Lost, Book 2, p. 32; p. 123, “why am I so changed,” Beelzebub, “O how fall’n,” in Paradise Lost, Book 1, p. 11; p. 170, “saved,” I Cor. 3:15; p. 173, “don’t judge,” Matt. 7:1; p. 175, “if God afflict your enemies,” Ps. 55:19, 22; p. 175, “an eye for an eye,” Ex. 21:24; p. 224, “Slough of Despond,” British Christian John Bunyan’s Pilgrim’s Progress (1985) Barbour and Company Inc., New Jersey, p. 9 etc.; p. 310, “conscience has turned,” Milton’s, Book 4, Satan, “for within him hell,” p. 78, and the monster in British atheist Mary Shelley’s, wife of British poet atheist Percy Shelley, (1818, 1823, 1831 editions) Frankenstein (a commentary of morality opposing Jesus’ modeling), “I like the arch-fiend bore a hell within me,” Penguin Books (2003), London, 16th chapter or Vol. 2 Chapter VIII, p. 138.

Can read 16^th chapter at http://www.authorama.com/frankenstein-20.html

74 Vintage Books (1994), New York, pp. 721-733. A prophetic novel on the coming end of Christian Russia due to increasing communist beliefs based on demonic nihilism. Their societal rejection of Jesus’ modeling can be seen in individual rejection, especially by the monster, in Shelley’s Frankenstein (see endnote 73). Demons has three parts with two epigraphs, p. XV, XVI, and 3; the first from Alexander Pushkin's (1830) poem also titled Demons and the second from Luke 8:32–36. Pushkin’s poem, Demons, follows.

In bygone days when life's array -
The sweet song of the nightingale
And maidens' eyes, the rustling woods -
Still left a fresh impression on me,
When loftiness of feeling,
And freedom, glory, love
Artistic inspiration
So deeply stirred my blood,
My times of hope were cast in shade
And pleasure dimmed by longing,

For it was then an evil genius
Began to pay me secret visits.
Our meetings were quite dolorous:
His smile, his glance mysterious,
His venom-filled and caustic sermons
Poured frozen poison in my soul.
With endless slandering remarks
He tempted Providence;
He claimed that beauty's but a dream;
Felt scorn for inspiration;

He had no faith in love or freedom;
He looked on life with ridicule-
And in the whole of nature
He did not wish to praise a single thing.

NOTE: Undeniable proof of the existence of demons and their characteristics is due to sola Scriptura from the undeniable proof of God’s existence. See https://systematicpoliticalscience.com/philosophiae.html

79 Not surprisingly this bizarre heretical proposal is from Christ denier homosexual supporters.

https://www.huffpost.com/entry/jesus-the-first-transgend_b_10006134

Jesus’ DNA was made by the Holy Spirit (Matt. 1:20; Gal. 4:4). He is the second Adam with pre-sin DNA (I Cor. 15:45-47).

95 https://www.actuaries.org.uk/system/files/documents/pdf/fractals.pdf

Thanks is extended to the Center for Strategic and International Studies (CSIS) for the event invitation in May, 2021. CSIS hosted the Nuclear Threat Initiative (NTI) featuring former US Senator Samuel Nunn of the CSIS, former US Ambassador to the UN for organizations Laura Holgate of the NTI, and US Army War College professor in the Department of National Security Frank Jones.

Righteous Fractals Topology of Human Hodological Spaces: Forming an Archetype Picture of Christ Jesus

by Dallas F. Bell, Jr.

by

Dallas F. Bell, Jr.