- What is a Fractal?
- Fractal in the Universe.
- Fractal in Human Behavior.
- Stories as Old as Time.
- Breaking Unwanted Fractals Through Self-Awareness.
What is a Fractal?
A Fractal is a type of mathematical shape that are infinitely complex. In essence, a Fractal is a pattern that repeats forever, and every part of the Fractal, regardless of how zoomed in, or zoomed out you are, it looks very similar to the whole image. Fractals surround us in so many different aspects of life.
Fractals are seen in the branches of trees from the way a tree grows limbs. The main trunk of the tree is the origin point for the Fractal and each set of branches that grow off of that main trunk subsequently have their own branches that continue to grow and have branches of their own. Eventually the branches become small enough they become twigs, and these twigs will eventually grow into bigger branches and have twigs of their own. This cycle creates an “infinite” pattern of tree branches. Each branch of the tree resembles a smaller scale version of the whole shape.
Another incredible place where Fractals are seen is in the circulatory and respiratory system of animals. If you take the human respiratory system, you will see a Fractal that begins with a single trunk (similar to the tree) that branches off and expands into a much more fine grained network of cavities.
We’ve all heard that every snowflake is unique and one of the contributing factors to the uniqueness of snowflakes is that they form in Fractal patterns which can allow for incredible amounts of detail and also variation. In the case of ice crystal formations, the starting point of the Fractal is in the center and the shape expands outward in all directions. As the crystal expands, the Fractal structures are formed in each direction. Just like the other examples of Fractals we have shared above, each iteration of the shape gets smaller and more detailed, which also contributes to the overall complexity of the shape.
Next time you eat a salad, a pineapple, broccoli, or a handful of other foods, you are actually eating a Fractal! Plants and leaves, just like animals, have internal structures that distribute nutrients through a network of Fractals. These structures allow for easy distribution of liquids and other life sustaining materials to travel through the plant and support the life of every cell.
Beyond the cellular level, some types of plants themselves are very Fractal in look. One of the most notable examples is a type of broccoli called Romanesco broccoli. This type of broccoli has an incredible structure of spires which emanate from a single source (similar to the Fractal Snowflake) that in turn have their own spires which continue on to the tip of the plant.
A fern is another great example of a Fractal. Ferns are essentially made up of the same general structure repeated over and over again.
Fractal in the Universe
The Fractal Geometry of the Universe
Abstract
A simple fractal pattern is studied that seems to reproduce the seemingly complex geometric patterns that appear in our Universe including supernova, planetary nebula and galaxy formations. The Mandelbrot set fractal construct is also shown to reproduce quite accurately the many shapes of galaxies and galaxy clusters. Some of the more complicated shapes like the Sting Ray Nebula and Cartwheel Galaxy can be easily reproduced using the simplest of fractal formulas.
Generating the Fractal Template
The fractal structure that I will be describing here is one of the simplest fractal algorithms that I have ever developed. Being a computer scientist, I have explored all the fractals, in particular the famous Mandelbrot Set fractal construct, which I have studied intensely since the mid 1980’s. I will be getting into that a bit later. For now, I will describe how to generate very simple fractal pattern based on two intersecting circles.
Start with a unit circle at a point in space (ie. radius = 1.0). Add another circle offset by x. Find the two intersection points of the circles.
To generate the fractal structure we must now recursively scale, rotate and translate.
First we double the radius (scaling).
Draw a circle with new radius at both intersection points (translate).
Find the two intersection points of these new circles (rotate 90).
Note: rotating by 90 is the same as multiplying by i.
Repeat.
When you study this fractal structure, you can see it has a lot of interesting features. The first thing you might notice is that the spheres on the inside, are completely enclosed by the intersection region of the two larger spheres. In other words, the smaller scaled spheres do not intersect with the larger scales spheres. This allows different scales behave independent of the other scales. I think this is an important feature of this particular fractal. The other thing that becomes apparent when you study this structure is that it allows one to JUMP from one scale to the next very easily at the points where the differently scaled circles are touching. This structure appears to be related to the famous phi spiral as seen below which should come as no surprise to the audience.
Spiralling IN using this Fractal Template.
The famous Phi spiral.
Here is an image of Supernova 1987A. Notice the similarity between the dynamic of this exploding star and the fractal pattern described above.
Here is the image of the Hourglass Nebula next to the fractal template pattern, oriented slightly different to match the orientation of the nebula.
Optionally we can add a circle of the same radius to the origin at each scale:
Generating this fractal pattern:
Here is an image of the Helix Nebula along with a modified version of the fractal template pattern. Notice the region near the top of the Helix Nebula, which corresponds nicely to the arch near the top of the fractal template on the right. The “eye” shape in the nebula matches accurately with the “eye” shape in the fractal template as well. Helix Nebula (NGC 7293) Visible Light
Here is another image of the Helix Nebula taken in the infrared spectrum. The arch near the top is clearly visible in this image. Helix Nebula (NGC 7293) Infrared Light
Here’s an example of a barred spiral galaxy. Notice how the spiral arm geometry matches exactly with the geometry of the fractal geometric figure. Barred Spiral NGC 1300
Here again, the eye shape and orientation and the spiral arms geometry matches quite well with the fractal template geometry. The Coiled Galaxy NGC 1097
Notice the similarity in shapes of these two objects. Whirlpool Galaxy (M51)
The Electron
The first movie of a single electron’s motion was made at Lund University, Sweden. It shows how an electron rides on a light wave after being pulled away from an atom. Notice the similarity between this shape and the shape of my fractal template diagram. Unfortunately, this is the only “real” photograph that I could find of an atomic element, so an extensive comparison cannot be made, however, the fact that this matches so nicely to the fractal template pattern is suggestive of the idea that the universe is fractal at all scales.
Fractal in Human Behavior
Market Mind Games: A Radical Psychology of Investing, Trading and Risk
Freud’s Fractals
Freud originally articulated the well-accepted psychological phenomena known as “transference” and the “compulsion to repeat.”
Transference simply means to move something from one place to another. In life, the concept refers to the fact that we apply what we learned about ourselves, our relationships to important people in our lives, and our perceived role in the world when we were young, to our perception of what is happening in our adult lives.
Fractals scale and, likewise, transferences scale. Each can be very precise but due to the complexity of human interaction and perception, rough at the same time. Like the patterns in broccoli and other plants, the repetitive patterns may not be 100% identical but they are so close that in practicality, they might as well be. Just the fact that anyone can see fractal patterns in ferns or human lungs obviates the need for an identical match.
When it comes to our psyches, eventually, if we peel back all the layers, sooner or later, the core fractal usually turns out to be our feelings about ourselves in relationship to our mothers. Think about it, they do give us our first feelings of self-worth or lack thereof. They are the first ones to respond or not respond to us. Many think the baby has no awareness or nothing that will stick with them when, in fact, the brain is developing based on the experiences it is having at the fastest rate it ever will.
When we first begin to look at our unconscious patterns, we probably shouldn’t go directly to Mom. It’s easier and more productive to pass through the layers of our history (and by definition our psyche’s development) of our fathers, siblings, and other important people like coaches and teachers and events from our school years. We typically think that somewhere along the way, we discarded all of that and replaced it with a new set of “adult” lessons. In actuality, without working to become conscious of what simple fractal elements were built within our minds, we experience the present through the lens or prism of the past experience.
If you think about brain development, this is not so startling and of course makes sense. We build on the knowledge and experiences we have learned before, year after year after year, beginning logically at conception or shortly thereafter. This is a biological fact. Mother Nature meets the brain. Could it be any other way? The small pattern, the simple fractal, repeats itself because the memory traces laid down early on merge together to form the foundation of our temperaments, personalities, and character—or the multifractal design of human nature. Over the years, I have called what I now know to be a fractal element in the development of the human adult psyche by many other names, such as:
- Echoes
- Emotional architectures
- Emotional templates
Echoes referred to the idea that we all have an internal echo, originally developed in childhood, of what our self-worth is. We hear the criticisms, spoken or unspoken, of our teachers, siblings, fathers, and mothers. And even if they didn’t overtly criticize us, because children are narcissistic by nature (i.e., they think the world revolves around them), anything that happens that is bad (an argument, a divorce, an accident), they attribute to or blame themselves. Given the emotional import, the self-blame remains. The latter becomes an internally generated criticism and ends up influencing us in ways even more hurtful than an externally sourced one.
Initially, the characteristics of these special relationships interact with the substrates in our brain to create an emotional architecture, a style of being and reacting. Like architectures and templates, years later, our unconscious minds follow the rules of the architecture or template while often hearing the self-talk that remains as an echo of earlier explicit criticisms.
Neuroscience and the Unconscious Fractal Feeling Context
To put it in the words of another team of researchers, Tamietto and de Gelder, “There is now increasing evidence that non-consciously perceived emotional stimuli induce distinct neurophysiological changes and influence behavior towards the consciously perceived world.” In other words, you may have no idea that you’ve been induced to feel this way or that but your body does. It signals inside your psyche and alters how you react. In the case of people dealing with market decisions, the induction occurs by the behavior of the price or the net effect on our profits and losses, but over and over, we deal with “non-consciously perceived emotional stimuli.”
Since I have been consulting on Wall Street, I have yet to find someone who habitually fights trends that doesn’t ultimately reveal a very clear and specific reason that arises out of their personal and family history. The easiest ones are traders who can notice that they want to prove they are smart.
This is actually true for me. As a person who's born alongside two brothers, one older and one younger with only 1 year difference each. I was compared a lot in my childhood. It's not inherently bad because I understand my parents intent is laced with "motivation". It's destructive in nature to be honest, because there's also a psychological "button" for me that I really come to hate when I'm compared to other people. To introduce the context of psychological button:
Emotional: How Feelings Shape Our Thinking
A more complex mental reflex is the psychological "button", the often-intense reaction we may have to certain social encounters. Just as your knee jerks when your knee tendon is taped, a psychological "button" can be pushed when a triggering experience draws you back into some unhealed issues from your past. Some common triggers are if someone ignores you, or doesn't follow the rules, or lies to you, or criticizes you, or uses a phrase such as "you never" or "you always." Whether or not emotion was involved in the formation of the trigger/response cycle, if such an event produces an immediate unthinking reaction, that's the mental equivalent of the knee-jerk reflex.
Clinical psychologists run into this all the time; buttons can create havoc when they are pushed by our colleagues, friends, and family. Even in otherwise healthy relationships, they can result in repeated cycles of conflict. Once we learn our friends' and family members' buttons, it is wise to avoid pressing them. Once we realize we have buttons ourselves, it is wise to avoid pressing them.
There were many layers of emotions that came from my own personal and subjective experience when I was intensly compared to other people. Think about the phrase "If they can do it, why can't you?" or "How come you can't do the things that those person can?" These repeated phrases, if overexposed, can totally affect the ego/esteem. My mom is what people call to be "Tiger Parenting", quoting the definition from Verywell Mind:
Tiger parenting is a strict parenting style that pushes children to excel academically at all costs.
Specifically, tiger parents tend to micromanage their children’s lives in ensuring they meet their high expectations. There is little to no room for the child to negotiate how their days are planned as the tiger parent will respond in a “because I said so” manner.
The approach includes limiting the child’s socialization with friends in favor of studying and/or participating in high-status extracurricular activities, using emotional threats and corporal punishment when the child misbehaves, lacking trust in the child’s ability to make decisions on their own, and disrespecting the child’s privacy.
[...]
Lack of autonomy for the child: Tiger parents have full control over their child’s life. The child is raised to make decisions based on the approval of their parents. There is no emphasis on self-regulation or independent thought. Tiger parents have no patience and/or desire to understand and get to know the child’s personality, thoughts, feelings, and perspective as a unique individual. It is expected that the tiger parents’ dreams are also the child’s dreams.
It's a somewhat common thing in some parts in Asia, especially China. It's in a sense, a brute-force methods using logic and rationality while to some extent abandoning all mental consequenes that can surface.
It also caused the origin of my love towards autonomy and freedom in decision making. Though the older I got, I was brave enough to tell them "what happened" through intense self-reflection and exercising my self awareness and tell them that I need privacy as my right, autonomy in my decision making, the nature of regret in life as when one kept making decisions laid by other people. It's a somewhat of a good ending story of that conflict with me and my parents about that, I don't know if I can speak of the same with people who experienced the same.
Feelings resurfaces, yet Self-Awareness is conquering those emotions and the fractality of the behavior.
Stories as Old as Time
As Freud explains in his essay, “Beyond the Pleasure Principle,”:
People all of whose human relationships have the same outcome: such as the benefactor who is abandoned in anger after a time by each of his proteges, however much they may otherwise differ from one another, … or the man whose friendships all end in betrayal by his friend; or the man who time after time in the course of his life raises someone else into a position of great private or public authority and then after a certain interval, himself upsets that authority and replaces him with a new one; or, again, the lover each of whose love affairs with a woman passes through the same phases and reaches the same conclusion.
Story of Infidelity
This story is as OLD as TIME. As people say "Once a Cheater, Always a Cheater" as I quote an article from choosing theraphy:
Although many people believe in the adage, “Once a cheater, always a cheater,” it is not necessarily true. Not every person who cheats once will cheat again. However, serial cheaters are people who seek out sexual partners on a continual, chronic pattern of infidelity.
Typically, these are people in committed, monogamous relationships who continue to purposefully seek extramarital romantic and/or sexual relationships. Despite the repetitive cheating, serial cheaters rarely suffer from feelings of remorse or guilt, because they often don’t look at cheating as a mistake.
and an article and research from University of Denver, Once a Cheater, Always a Cheater? DU Study Examines Serial Infidelity, 2018 based on a research from "Once a Cheater, Always a Cheater? Serial Infidelity Across Subsequent Relationships"
[Kayla Knopp] recently released study, “Once a Cheater, Always a Cheater?: Serial Infidelity Across Subsequent Relationships,” contains some jarring findings. For one, 40 percent of unmarried couples report infidelity. Worse: cheaters are more likely to cheat with future partners. Worse still, those who are cheated on are even more likely to endure similar heartbreak.
“The past matters for relationships,” says Knopp, who will graduate with a PhD in clinical psychology in May. “What we do at every step along the way in our romantic histories ends up influencing what comes next — whether that’s infidelity or cohabitation or a bunch of other relationship behaviors. That history tends to come with them.”
As a researcher who specializes in romantic commitment, Knopp has read plenty of papers on unfaithful partners. What consistently went missing, she realized, was data on serial infidelity. In other words, will the cheat repeat?
Fortunately, Knopp had at her disposal five years of data compiled by psychology research professors Galena Rhoades, Howard Markman and Scott Stanley. With collaboration from this DU team, Knopp was able to track 1,600 individuals from relationship to relationship and examine their behavior. She found:
- Someone is three times more likely to cheat if they have cheated in the past.
- A person is two to four times more likely to be cheated on if they have been cheated on or have suspected cheating in a prior relationship.
- Men and women are equally likely to cheat or be cheated on.
- A person's likelihood of cheating is found, not in a single demographic characteristic, but in a complex combination of factors, including cultural values and available partners
[...]
“Hopefully, by identifying risk factors, then that gives people a little more power and control in their own lives,” she says. “That might be really important to discuss, so we can plan ahead to avoid unwanted outcomes in the future.”
People would call me a "cynic" or "one dimensional" if I were to blatantly agree that "Once a Cheater, Always a Cheater" to a friend that confessed to me that they have been cheated. So I laid out to them the statistics that have been studied in the past. If "Someone is three times more likely to cheat if they have cheated in the past," then people are always welcomed to take the odds. They have made a conscious decision to stay and that's the end of it, cases like these are always case by case and I don't make the decisions for them.
Story of "Retarded Degenerate Gambler"
There's a quite recent "phenomena" that someone appears to lose 200k and even his own nametag is "Tarded Degen Gambler". It's so fucking ironic
Jesus christ man, its the SECOND OF JANUARY. How the fuck you fumbled so fucking hard.
Fella proceed to beg for donation money on PUBLIC TWITTER DOT COM and proceed to enter trading again and got LIQUIDATED AGAIN THE NEXT DAY.
Leverage trading is such an interesting enabler to this behavior. The story that is old as time that this isn't just the first time I've seen this being PUBLICIZED ONLINE AS A MEAN TO VENT. Most people "lose everything" not because bitcoin dropped -100% in value, rather fella loses -100% of his portfolio when BTC crashes by only -10% (small in comparison to -100%). This is allowed by the nature of leverage trading. As I quote an article from BitPanda, What is Leverage Trading
Leverage trading is a high-risk/high-reward trading strategy that experienced investors use with the aim of increasing their returns. Generally speaking, leverage trading allows investors to gain exposure that they normally wouldn’t have, however it also entails a high degree of risk.
Profits and losses are calculated based on an investor’s total exposure. Exposure refers to an investor’s potential risk, i.e. how much money they stand to gain or lose from an investment.
Leverage trading enables investors to trade with more exposure than the amount they invested, i.e. how much they stand to gain (or lose) is worth more than the money they put in. This is usually available in multiples like x2, x5 or x10, meaning an investor’s exposure is double, five times, or ten times the amount of money they initially invested. Doubling one’s exposure could potentially double one’s returns, however if the investment falls through (i.e. if the value of an asset goes in the opposite direction of one’s leverage position) then the losses are also doubled.
The weird fucking thing is that, how are they not aware that they are losing money and kept doing the same thing? The Fella is aware that he is losing money but I think fella does not have high self awareness to stop it from becoming again.
There were a screenshot that he posted on how his portfolio worth was grinding down from 200k to 0. As he puts on the caption of the tweet "All of this happened in the span of 2 hours by the way. This is where I have a gesture of "Fuck, this guy is well aware that he can lose 200k if he chooses not to do anything, but why didn't he do anything? Did he choose not to do anything? Was he just praying for something to happen?"
The Fractality or "Reoccuring Patterns of Retarded Degenerate Gambler"
One of the big reason why I grow an affinity towards crypto trading is due to the "availability of data" in this context, data represents market participants behaviors, human behaviors.
I need to walk you through the mechanics on how the behavior of "Retarded Degenerate Gambler" can appear in public data. The starting ways is to understand how Retarded Degenerate Gambler can lose $200k on a 10% downward move to begin with. When he said he's liquidated, it means that he was forced to liquidate his positions. What does it mean to force liquidate? Why does it happen? When someone entered a leveraged position, coming from this explanation:
Leverage trading enables investors to trade with more exposure than the amount they invested, i.e. how much they stand to gain (or lose) is worth more than the money they put in. This is usually available in multiples like x2, x5 or x10, meaning an investor’s exposure is double, five times, or ten times the amount of money they initially invested. Doubling one’s exposure could potentially double one’s returns, however if the investment falls through (i.e. if the value of an asset goes in the opposite direction of one’s leverage position) then the losses are also doubled.
Say 10x leverage, it is true if Bitcoin moves upwards 10%, fella with a position 200k, will fucking gain a profit of 200k, out of only a mere 10% move. But the downsize risk remains of the same. If bitcoin moves downwards 10% fella will lose 200k because 10% move * 10 (leverage) means 100%. Simple maths.
Now this is between the drive theory versus the pleasure theory. Whereas the drive theory says that people are motivated principally by the desire to avoid unpleasant feelings, such as hunger and thirstsrc. While the pleasure theory says that people are motivated principally by the desire to experience pleasant feelings.
Now there is both synchronizity and Inconsistencies when these two theories merge. One can say that Retarded Degen Gambler or RDG for short, is motivated to lift himself up out of poverty in which poverty is unpleasant. No one wants to work a job (presumably) a job that one doesn't like, one would (if given an option), to do things whatever they want, whenever they want. But we are already wired for obligations through responsibilities, liabilities that comes with money and jobs. Chasing money through trading and clicking buttons and see "money gained" in context of a winning trade is psychologically pleasurable, especially seeing mind boggling numbers of wealth that quite distorted one's perception, as in "Oh, I just gained sums of money that is worth of 2 months of my 9-5 or even sometimes worth 12 months worth of 9-5s, accounting that one does not like its job, gaining this much sums of money is what I would coin "highly pleasurable." Cognitive dissonances must happen only when one realized that there's risk implied on the pleasure seeking tendency yet chooses instead of acknowledging it and taking proper actions, but chooses to go down the road of self-deception. "Ah it's going to be okay, there's no way this hits my liquidation price." Until it hits it.
Every trader that participates in leverage trading knows what it really means when price hits their liquidation price. It's over, no bueno, zero, nada. Yet how come I see on my timeline after 3 years of trading the same thing happened over and over again, being done by different people from time to time. The story is always of the same. It reminds of me to the fractal nature of the brain that materializes in fractalneralized behavior that I want to write this article to immortalize this essay or thesis. Like the case of infedility on how a person who cheats is more likely to cheat again, is it really a way out of this pattern?
I think there is, and that is only through exercising self awareness.
Breaking Unwanted Fractals Through Self-Awareness.
LaPlanche and Pontalis, explained in psychoanalytic terms the origin of this phenomena that seems unconscious and the illusion of uniqueness of the moment:
The compulsion to repeat is an ungovernable process originating in the unconscious. As a result of its action, the subject deliberately places himself in distressing situations, thereby repeating an old experience, but he does not recall this prototype; on the contrary, he has the strong impression that the situation is fully determined by the circumstances of the moment. These patterns acquired in childhood are forgotten and are instead acted out and repeated in life. It is reproduced not as a memory but as an action.
If we were to see each of our "tragedy" or rather "unwanted circumstances" through our own eyes as a mean of "self-refelction" and account things "as it is". Note, that I heavily emphasize as it is, because the heat of the moment, it is much reflesive or rather "easy" for our brain to say "ah that couldn't possibly be me, they were just the asshole and they deserve what they got." Or rather the more comical example of how "Retarded Degen Gamble" blame the market and demonizing the market instead of facing the person who puts itself to the circumstances to begin with, himself. "Price is not going to hit my liquidation" is a mere confession that oneself is not prepared and is decepting himself. Then the pattern begins THE NExT FUCKING DAY.
If we were to see "tragedy" or "unwanted circumstances" to a box and see every item on the box at is as how the accidents ravelled. As for my own example, how my parents at one unfaithful night screamed and yelled at me that they don't love me and wished that I were never born had they know I would turn to be such a child when I was a kid that quite rang inside my head from time to time in adulthood as a voice that increases the void of belonging. I saw the box of tragedy and the "items" that were inside of the box and how it came to being. It is true that I fucked up a lot that night, it is true that there were heat of the moment and sensations of anger, frustration, and disappoinment that drove the words from my mother's throat. As I observe my mother do the things that she does the following days and weeks. Does a mere words of "I don't love you" even matter when she does the acts that shows that she loves me? Verbal act is a form of action, physical action that shows attributes of devotedness out of love and care is also another thing, we can see both of these "items" as it is and give weight to each of the item.
I still have psychological buttons, for example when I'm compared frustatingly with another person, I feel that there's a gap between my current self and what the other person expects me to be. The feeling and sensation that comes from "Oh... Am I really and whatever I've already done is not enough?" "What is enough for you?" "If I just become that person and only then you will be happy? Mom and Dad?" The void of belonging that shrieks for fullfillment that dictates the road of the formation of one self. I still need to see and analyze things as it is to decipher what it means to be compared and only then I agree how the conversation that I was compared, materialized. I was in fact, disappointing my parents, I was in fact, done the things that my parents did not expect me to do, my parents was in fact disappointed because they wished that I did not the things I've done or rather what I've done is not enough and they were just concerned about my future. Emotions and sensations that arise still doesn't lie and reveals itself like an unstable uranium that lashes out feelings of discomfort and uneasiness that myself is not enough and I can't disappoint other people or make them sad, the perpetual cycle of sadness from an instance that lives in memory where emotions were intensely distilled.
There's undeniably a repeating patterns of my behavior that surfaces from previous experience or rather emotions from memory. There are good and bad behaviors but most importantly, we can't change the past that have warped the sense of our current self. But through self awareness we can leverage on how those experiences can be something of meaning to us, regardless how hurt we were. I was and maybe still am, a person who struggles to have an identity, I was constantly compared to other people "Why can't you be more like your brother?" "Why don't you participate in this competition?" "Why can't you stop doing the mistakes that you've done and oh there's so many mistakes that you've done." These phrases are the fuels of my cravings toward "Self Identity". "What the fuck am I really am?" Then it pushed me to write all of these articles that I find meaning of and other people that have read it find meaning within. I did not follow my parents blindly, rather I asked myself why do they think it's the best for me to follow the advice that they have given me. The hypercriticalness of awareness that drove to understanding things that made people like the things I've created and the strong want to mark one's existence as something excellent and useful for other beings. Just like a good trader that learn from their mistakes and stop losing money and be constantly profitable, it starts from analyzing their "tragedy" or "unwanted circumstances" that happened instead of blaming the market or rather the external that the circumstances happened to them but not someone else. The good trader can finally be free from the fractal of losing money consistently and start making actual money from trading.