Fractal Phenomenon Proves Simulation Hypothesis?The humanity is accelerating towards the times when virtual worlds will get so realistic that their inhabitants gain consciousness without realizing they exist in a simulation. The idea that we might be living in a simulation was widely introduced in 2003 by philosopher Nick Bostrom. He argued that if the civilization can create realistic simulations, the probability that we are living in one is extremely high.
Modern games only render areas that the player is observing, much like how reality might function in a simulation. Similarly, texture of game environments update as soon as they are viewed, reinforcing the idea that observation determines what is rendered.
QUANTUM MECHANICS: The Ultimate Clue
Quantum Mechanics challenges our fundamental understanding of reality, revealing a universe that behaves more like a computational process than a physical construct. The wave function (Ψ) describes a probability distribution, defining where a particle might be found. However, upon measurement, the particle’s position collapses into a definite state, raising a paradox: why does the smooth evolution of the wave function lead to discrete outcomes? This behavior mirrors how digital simulations optimize resources by rendering only what is observed, suggesting that reality itself may function as an information-processing system.
The Born Rule reinforces this perspective by asserting that the probability of finding a particle at a given location is determined by the square of the wave function’s amplitude (|Ψ|²). This principle introduced probability into the very foundations of physics, replacing classical determinism with a probabilistic framework. Einstein famously resisted this notion, declaring, “God does not play dice,” yet Quantum Mechanics has since revealed that randomness and structure are not opposing forces but intertwined aspects of reality. If probability governs the fabric of our universe, it aligns with how simulations generate dynamic outcomes based on algorithmic rules rather than fixed physical laws.
One of the most striking paradoxes supporting the Simulation Hypothesis is Schrödinger’s Cat, which illustrates the conflict between quantum superposition and observation. In a sealed box, a cat is both alive and dead until an observer opens the box, collapsing the wave function into a single state. This suggests that reality does not exist in a definite form until it is observed—just as digital environments in a simulation are rendered only when needed.
Similarly, superposition demonstrates that a particle exists in multiple states until measured, while entanglement reveals that two particles can be instantaneously correlated across vast distances, defying classical locality. These phenomena hint at an underlying informational structure, much like a networked computational system where data is processed and linked instantaneously.
Hugh Everett’s Many-Worlds Interpretation (MWI) takes this concept further by suggesting that reality does not collapse into a single outcome but instead branches into parallel universes, where each possible event occurs. Rather than a singular, objective reality, MWI posits that we exist within a constantly expanding system of computational possibilities—much like a simulation running countless parallel computations. Sean Carroll supports this view, arguing that the wave function itself is the fundamental reality, and measurements merely reveal different branches of an underlying universal structure.
If our reality behaves like a quantum computational system—where probability governs outcomes, observation dictates existence, and parallel computations generate multiple possibilities—then the Simulation Hypothesis becomes a compelling explanation. The universe’s adherence to mathematical laws, discrete quantum states, and non-local interactions mirrors the behavior of an advanced simulation, where data is processed and rendered in real-time based on observational inputs. In this view, consciousness itself may act as the observer that dictates what is “rendered,” reinforcing the idea that we exist not in an independent, physical universe, but within a sophisticated computational framework indistinguishable from reality.
Fractals - Another Blueprint of the MATRIX?
Price movements wired by multi-cycles shaping market complexity. Long-term cycles define the broader trend, while short-term fluctuations create oscillations within that structure. Bitcoin’s movement influencing Altcoins exemplifies market entanglement—assets affecting each other, much like quantum particles. A single event in a correlated market can ripple across the entire system like in Butterfly effect. Just as a quantum particle exists in multiple states until observed, price action is a probability field—potential breakouts and breakdowns coexist until liquidity shifts. Before a definite major move, the market, like Schrödinger’s cat, remains both bullish and bearish until revealed by Fractal Hierarchy.
(Model using Weierstrass Function )
A full fractal cycle consists of multiple oscillations that repeat in a structured yet complex manner. These cycles reflect the inherent scale-invariance of market movements—where the same structural patterns appear.. By visualizing the full fractal cycle:
• We observe the relationship between micro-movements and macro-structures.
• We track the transformation of price behavior as the fractal unfolds across time.
• We avoid misleading interpretations that come from looking at an incomplete cycle, which may appear random or noisy
From Wave of Probability to Reality
1. Fractal Probability Waves – The market does not move in a straight line but rather follows a probabilistic fractal wave, where past structures influence future movements.
2. Emerging Reality – As the price action unfolds, these probability waves materialize, turning potential fractal paths into actual price trends.
3. Scaling Effect – The same cyclical behavior repeats at different scales (6H vs. 1W in this case), reinforcing the concept that price movements are self-similar and probabilistically driven.
If psychology of masses that shapes price dynamics is governed by mathematical sequences found in nature, it strongly supports the Simulation Hypothesis
Do you think we live in a simulation? Let’s discuss in comments!
Cycle
AAVE - DeFi leader
As I have stated in my previous analysis AAVE is one of the leaders in DeFi sector, and stays quite underpriced still. Just as I predicted, it reached my target and now I think it will go for .618 Fib. After that in theory there also will be a correction.
But if you look at Solana chart, it has gained a lot of attraction in this cycle and has made a new ATH. I think AAVE will be one of the few Altcoins which have the required potential to make new ATH also. Let's hope and monitor
BTC - Time cycles unlock some key insights BTC is very clearly able to be carved out into time cycles, or 'Hurst' cycles, which are regular appearing patterns of units of time which can help us in informing price action. Looking at BTC, it's clearly cutting into cycles of about 40 days with the price action within each cycle very clearly going in either direction - apart from one! Looking at the most recent cycle we just entered into, the price action is likely to rise and continue to rise until either the middle of the cycle (target) or the end of the cycle (vertical line). So please add Hurst cycles to your cocktail of methods for understanding 'when' an event is likely to take place, or at least give you a marginally higher percentage probability. Good luck. Follow and share for more.
Nat Gas: Heating Up into the WinterBrief Overview on Natural Gas
Natural Gas is a commodity generally traded on the premise of weather forecasts indicating cooler or warmer seasons. This allows traders to speculate on demand for the product as it generally trades higher with cooler temperatures. Today we are looking at the weekly chart.
Thesis: Technical Analysis Pointing to a Bounce
This analysis is mainly focused on the lasting demand zone that Natural Gas time and time again respects and typically bounces from. The weekly chart points to the likelihood that the R/R is favorable for a long position at these levels in the 2.20's. Not only do we see NG tap back into this heavy demand zone, but we also can see a Cup & Handle on the weekly chart signaling potential greater upside.
Demand Zone offers strong R/R as it dips back in to these levels.
Cup & Handle can represent even further upside, but will rely on the initial rebound to prompt the possibility of it playing out.
There is also a trendline (not pictured) that is supporting the current bounce we are seeing today from the 2.18/2.19 level. It is important to note that the commodity has been seeing higher lows since the Spring.
Lastly, a tap of fundamentals play into this idea as well. Though winter demand is always priced in, this year forecasts have repeatedly painted the picture that this winter will be historically mild. Due to these forecasts implying less seasonal demand for Nat Gas, a shift in the shorter-term and more accurate models as we approach the winter season will sharply move the price of Nat Gas and represents that the current price is truly pricing in a very mild winter. This basis supports the idea of great R/R on this LONG trade idea.
Disclosure
I am currently in a long position in Natural Gas after entering on the Friday (10/18) Close
My position includes: AMEX:UNG Credit Spread 13/12P , AMEX:BOIL common shares
If this thesis holds up, I would plan to roll my credit spread contracts into further expirys
Thanks for reading!
Not Financial Advice
2025 is a Bull Year I would like to start the year with what I expect if we talk about the crypto market - a bull market until September 2025
If we talk about the stock market - bullish or flat as it was in 2005 and 2015.
If we take statistics in years that end in the number 5 (1895, 1905, 1915, 1925, 1935, 1945, 1955, 1965, 1975, 1975, 1985, 1995, 2005, 2015) - we see bull markets.
Below, I have shown weekly charts of each year ending in the number 5.
1905
1915
1925
1935
1945
1955
1965
1975
1985
1995
2005
2015
2025
Here, we saw that all years are bullish, but 2005 and 2015 were reaccumulation.
Positive Scenarios for 2025
Soft monetary policy: If the Federal Reserve keeps rates at levels that support credit growth and capital availability, it will support the corporate sector and business expansion.
Technological breakthrough: A recovery in investment in artificial intelligence, green energy and biotechnology could create new growth drivers for the Dow Jones.
Sustainable global development: If geopolitical tensions diminish and international trade relations stabilize, the global economy will gain new momentum, reflected in the index's growth.
Negative Scenarios for 2025
Tight monetary policy: A sharp rise in interest rates could reduce the availability of capital, which could slow economic growth and pressure corporate profits.
Geopolitical instability: Increased conflict or trade wars between major economies could lead to declining investor confidence and capital outflows from the market.
Declining technological development: If leading sectors such as technology and green energy do not show the expected growth, it could affect market expectations and valuations.
Conclusion
Analyzing the history of the Dow Jones, years ending in 5 represent unique periods of growth and recovery. Against the backdrop of current macroeconomic and geopolitical conditions, 2025 could be a year of significant opportunity.
The optimistic scenario is based on continued loose monetary policy, innovation, and stabilization of global relations. However, the risks associated with tight monetary policy and global instability require caution.
For investors, 2025 could be a year of essential choices. Focus on long-term trends, analyze macroeconomic indicators, and diversify your portfolio. History shows that even in times of uncertainty, the market has the potential to grow.
And for years that end in number 7 according to bearish statistics, I will write about this in 2027
Best regards EXCAVO
Bitcoin's Ultimate Pump: The Trap Before the CrashBitcoin continues its “hype” and is close to forming the next spurt. Globally, the picture looks like close to the distribution zone. We are approaching the biggest “cheat” in history. I expect a final spurt into the zone around 120k, from here a long trade will start where altcoins will shoot up and show incredible gains. The crowd will be experiencing FOMO, heads of state and big companies will start making noise that this is just a pro-trade level for Bitcoin before the next spurt. Only the majority will fall back into the trap and end up in a bear market with huge losses. The market is set up so that only 10% will make money and the other 90% will be cheated. After the distribution is completed, I expect the bitcoin price to fall below the 0.5 Fibonacci level. The RSI value will drop below 30 units on such a drop and we will enter a global fear phase. I would attribute the next bull market to the rise of the DeSci and AI sectors. My research on the cryptocurrency market sectors shows that large funds and corporations are starting to invest in projects in these areas.
Horban Brothers.
SQ | Why Wallstreet is Bullish | LONGBlock, Inc. engages in creating ecosystems for distinct customer audiences. It operates through the Square and Cash App segments. The Square segment provides businesses the ability to accept card payments. The Cash App segment offers an ecosystem of financial products and services to help consumers manage their money. The company was founded by Jack Patrick Dorsey and James Morgan McKelvey in February 2009 and is headquartered in Oakland, CA.
PEPE, long term super cycle awaits!This is how PEPE could play out in the long-term assuming that we're putting in wave 1, which looks like a leading diaganol. In the medium term we're likely to see some lows as the minor wave 1 corrects for the clearly visible ABC. But, then hold on to your hats as we put in wave 3 which is always the most violent. If you're not out of your shorts by then, this pattern could ripe your face clean off. In any case, keep an eye and plan for early retirement. Follow for more.
DOGE price predictionI've posted a few DOGE coin predictions over the last few weeks, with this one being an adaptation of one that I've previously posted. It looks as though we could be in a handle of a very long term cup and handle, with the handle being wave 4 of 5 of 1. IF it plays out there there's a mid-term decline underway and still coming until the end of the current cycle and then up in typical impulse fashion for 1-5 for the completion of 5. But, if there is a local high, then the cup and handle is invalidated and I'll put in a new prediction. In the immidate term all crypto is likely to go down for at least another week and then up from there. Follow for more.
Post-Holiday BTC Rallies: A Historical PerspectiveIdea:
Over the past six years, Bitcoin has exhibited a fascinating pattern: post-Christmas rallies. Let’s dive into the data and analyze what this could mean for the market this time around.
Historical Context:
In 5 out of the last 6 years, Bitcoin has seen significant gains shortly after the holiday season, with price increases ranging from 44% to an astonishing 272%. These rallies have been a consistent part of Bitcoin’s cyclical behavior, making them an exciting opportunity for traders and investors.
Key Observations:
2017/18: BTC rallied over 272%, marking the peak of an explosive bull market.
2019/20: A solid 44% gain during the recovery phase from the bear market bottom.
2020/21: Post-pandemic bull run fueled a 122% surge as BTC climbed to new highs.
2021/22: A rally of 90%, driven by retail and institutional adoption.
2022/23: Another impressive rally of 72% as the market recovered from a bear cycle.
The only exception? 2018, the first phase of a brutal bear market, when market-wide sentiment was overwhelmingly bearish. This highlights a crucial insight: rallies are far less likely during early bear phases.
What About This Year?
📊 Cyclicality is Key: Bitcoin’s price action has always been heavily influenced by cycles. With the market in a recovery phase following the 2022 lows, we could be on the verge of another post-holiday rally.
📈 Factors to Watch:
Macro Sentiment: With inflation stabilizing and global markets recovering, Bitcoin is regaining strength.
Institutional Interest: Continued interest in BTC ETFs and large-scale adoption could fuel upward momentum.
Cyclical Patterns: The historical consistency of these rallies cannot be ignored.
Possible Scenarios:
1️⃣ Bullish Case:
If history repeats itself, we could see Bitcoin post significant gains over the next few months, potentially targeting new highs in 2025 as part of the broader bull cycle.
2️⃣ Bearish Case:
If macroeconomic factors or unforeseen events trigger a pullback, the rally might be subdued, or Bitcoin could enter a consolidation phase.
Why This Matters:
Understanding these cyclical patterns can provide a major edge for traders. The post-holiday season has been a lucrative time for Bitcoin in the past, and recognizing these opportunities could make all the difference.
What are your thoughts? Will Bitcoin repeat history this year? Or are we in for a surprise? Share your ideas below!
Bitcoin Dominance: Cycles and Post-Halving 2024 ForecastAn analysis of BTC Dominance in the context of market cycles and halving events. The chart highlights historical patterns of dominance decline following Bitcoin price peaks, which occurred 17 months after each halving. The outlined scenario suggests a potential return to key support (~41%) before a rebound.
Will history repeat itself? Let’s watch how upcoming market events shape BTC Dominance dynamics heading into 2025.
BTC - This Christmas is NOT different!Hello TradingView Family, this is Richard, and I want to wish you all a Merry Christmas.
I hope you enjoy this Christmas-themed idea.🎄
💡Can you spot a pattern here?
As shown in my last two Christmas posts (attached to the chart), BTC broke out of consolidation and surged by around 70%.📈
I believe this Christmas will be no different.
For the next bullish wave to begin, a break above the orange zone is needed, which aligns perfectly with the $100,000 round number.
What do you think? Will this Christmas follow the structure of the past two years, or will it be different and lead to a deeper correction⁉️
📚Always follow your trading plan regarding entry, risk management, and trade management.
And Remember: All Strategies Are Good; If Managed Properly!
Merry Christmas Everyone 🎄
~Richard Nasr
CRYPTO SUPER CYCLE 2024-2026:BEAR TO BULL ALL WHAT YOU NEED HERE🔄 CRYPTO MARKET CYCLES: MAJOR TRANSITION - FROM BEAR TO BULL 2024-2026
Technical Market Cycle Analysis:
- Current price: $346.31
- Clear transition from bear to bull market
- Three distinct cycles identified: BTC, ETH, ATLS
Market Phase Breakdown:
📉 Bear Market (2022-2024):
- Declining trend complete
- Bottom formation validated
- Accumulation phase ending
📈 Bull Market (2025-2026):
- BTC cycle initiating bull run
- ETH cycle following
- ATLS cycle completing the sequence
Key Observations:
- "Traders confusion" zones marked at critical transitions
- Clear cycle progression: BTC → ETH → ATLS
- Market structure showing higher lows forming
- Volume profile supporting bullish transition
⚠️ Critical Points:
- Major market cycle shift in progress
- Multiple timeframe alignment
- Clear cycle rotation pattern
- Historical pattern repetition
🔔 Market Intelligence:
- Bull market projected until end of 2026
- Three distinct crypto cycles identified
- Clear market phase transitions
- Institutional accumulation evident
#CryptoMarketCycles #BullMarket #TechnicalAnalysis #CryptoTrading #MarketPhases
Want detailed cycle breakdown? 📊FOLLOW ME
CYCLE 4 | LOG Trend Lines Chart - For Fun!Quick post looking at how BTC has historically respected 'log trend lines and how they may affect BTC future price action.
Will be fun to see how this model holds up over cycle 4 and future BTC cycles (view on a computer and use the future price action tools to see what happened past todays post date).
Distribution phase in the next 10 monthsSo we broke 100k. I'm sure we'll see higher in the next 10 months.
What's next? When is the correction?
I see such messages every day. That's why I want to give a full commentary and my vision.
As Waykoff told us, there are accumulation and distribution zones.
On top is the distribution zone If we stick to the theory of cycles, which I often write about
www.tradingview.com
We are entering the zone of local distribution I mentioned and marked with red zones If we are interested in the question how we will form the top and where we will distribute?
I would take into account the fact that we are already in the bitcoin distribution zone in this cycle and it will continue for another 10 months.
So, sideways in the 50k range, I agree, but I don't think it will go below the previous high of 73k.
Three distribution options:
1. ATH and then a gradual slide - the most standard top formation, with a run above 100k to induce euphoria
2. Two rising tops look better with liquidity removal of the first top, etc.
3. The killer of all the shorts, those waiting for the crisis, and so on.
They're going to kill all the non-believers on the moon.
And force everyone who believes in a million dollars for bitcoin to buy it.
Conclusion -
I expect a local distribution above 100k over the next 10 months, the possible top formation I have shown.
I do not expect a sharp drop to 50k - bitcoin has become a different asset class.
Everything can change a lot in 10 months, and based on my cycle theory,
I am waiting for the bull cycle to end. In this range of 10 months, altcoins will once again fall and rise at the very end. They will fall 51 more weeks down after September 2025.
I'm talking about local forecast in 1-2 years, further it will be even more interesting because globally after this cycle, all retail will say goodbye to their bitcoin and will not buy it back cheaper in 95% of cases. and Next we will count how much 1 sashoshi is worth.
in 1 Bitcoin is 120,000 satoshis.
When 1BTC reaches $120k.
1 sat = 1USD
And due to the fact that the printing press is working 1 satoshi will grow in the long run.
I hope for the best in our world. Stay close.
You can find out about other communication opportunities down below the chart.
Best regards EXCAVO
Alt Season is Right Around the CornerBitcoin dominance has been growing in the past few days as it outperforms the rest of the cryptocurrency market after the sharp drop last week. Many things are pointing towards Bitcoin continuing to outperform in the short term as we gear up for the next parabolic bull market.
However, alt season is very close and, once BTC confirms it's breakout towards 100k, a lot of the large caps like Ethereum and Solana will begin to go up very quickly. This is based on my cyclical analysis of alt seasons. To get a better idea of the cyclicality of cryptocurrency, Bitcoin, and alt seasons, check out my previous post which predicts the next parabolic rise in November:
An important thing to note when referring to alt seasons is that they don't last long (only a few months). So understand your timeframe when investing over the coming weeks. Another important idea is how money tends to flow during this period. It historically starts with Bitcoin breaking its all time high and beginning to rise. During this time, altcoins tend to underperform. But once BTC consolidates and begins to go sideways, that's when the rest of the market has time to catch up. In the chart I show 4 key points:
Bitcoin
This is when BTC makes a significant breakout whether that's from a significant resistance level or its ATH. This is where BTC is outperforming 99% of the market.
Ethereum & Large Caps
BTC will begin to slow down and a lot of the major altcoins will see a big increase. This is where you can find great trade setups on the BTC pairs like ETHBTC, SOLBTC, etc.
BTC Consolidates
BTC will start to go sideways, cooling off and preparing for its next rise. From here you might see some pumps in mid-low caps. These tend to be volatile and hard to predict.
Small caps - Quick and fast
As BTC continues to go sideways, some small caps might experience quick pumps in price. Similarly, these tend to be even more volatile and hard to predict.
After this, the pattern repeats back up to Bitcoin until we reach a peak and begin a new bear market.
The cryptocurrency bull market is brewing up and alt season can offer some incredibly profitable opportunities. Plan ahead, and don't overtrade.
New cycle beginsBitcoin is turning bullish on a weekly basis for the first time after a deep red bear market phase. This is a huge signal and usually indicates the beginning of the next cycle.
I have marked the deep red phase in purple and the first weekly signal with an arrow on the chart.
This is the first phase of the cycle, so I would not expect any crazy end-of-cycle moves. But for now, dips should be a gift from heaven. In the past we have seen 30-50% corrections within the cycle. So we need to be prepared for that as BTC approaches and breaks its ath.
We will have to figure out the target during the next year but I think it will be 6 digits.
Natural Patterns & Fractal GeometryIn my previous research publication, I explored the parallels between the randomness and uncertainty of financial markets and Quantum Mechanics, highlighting how markets operate within a probabilistic framework where outcomes emerge from the interplay of countless variables.
At this point, It should be evident that Fractal Geometry complements Chaos Theory.
While CT explains the underlying unpredictability, FG reveals the hidden order within this chaos. This transition bridges the probabilistic nature of reality with their geometric foundations.
❖ WHAT ARE FRACTALS?
Fractals are self-replicating patterns that emerge in complex systems, offering structure and predictability amidst apparent randomness. They repeat across different scales, meaning smaller parts resemble the overall structure. By recognizing these regularities across different scales, whether in nature, technology, or markets, self-similarity provides insights into how systems function and evolve.
Self-Similarity is a fundamental characteristic of fractals, exemplified by structures like the Mandelbrot set, where infinite zooming continuously reveals smaller versions of the same intricate pattern. It's crucial because it reveals the hidden order within complexity, allowing us to understand and anticipate its behavior.
❖ Famous Fractals
List of some of the most iconic fractals, showcasing their unique properties and applications across various areas.
Mandelbrot Set
Generated by iterating a simple mathematical formula in the complex plane. This fractal is one of the most famous, known for its infinitely detailed, self-similar patterns.
The edges of the Mandelbrot set contain infinite complexity.
Zooming into the set reveals smaller versions of the same structure, showing exact self-similarity at different scales.
Models chaos and complexity in natural systems.
Used to describe turbulence, market behavior, and signal processing.
Julia Set
Closely related to the Mandelbrot set, the Julia set is another fractal generated using complex numbers and iterations. Its shape depends on the starting parameters.
It exhibits a diverse range of intricate, symmetrical patterns depending on the formula used.
Shares the same iterative principles as the Mandelbrot set but with more artistic variability.
Explored in graphics, simulations, and as an artistic representation of mathematical complexity.
Koch Snowflake
Constructed by repeatedly dividing the sides of an equilateral triangle into thirds and replacing the middle segment with another equilateral triangle pointing outward.
A classic example of exact self-similarity and infinite perimeter within a finite area.
Visualizes how fractals can create complex boundaries from simple recursive rules.
Models natural phenomena like snowflake growth and frost patterns.
Sierpinski Triangle
Created by recursively subdividing an equilateral triangle into smaller triangles and removing the central one at each iteration.
Shows perfect self-similarity; each iteration contains smaller versions of the overall triangle.
Highlights the balance between simplicity and complexity in fractal geometry.
Found in antenna design, artistic patterns, and simulations of resource distribution.
Sierpinski Carpet
A two-dimensional fractal formed by repeatedly subdividing a square into smaller squares and removing the central one in each iteration.
A visual example of how infinite complexity can arise from a simple recursive rule.
Used in image compression, spatial modeling, and graphics.
Barnsley Fern
A fractal resembling a fern leaf, created using an iterated function system (IFS) based on affine transformations.
Its patterns closely resemble real fern leaves, making it a prime example of fractals in nature.
Shows how simple rules can replicate complex biological structures.
Studied in biology and used in graphics for realistic plant modeling.
Dragon Curve
A fractal curve created by recursively replacing line segments with a specific geometric pattern.
Exhibits self-similarity and has a branching, winding appearance.
Visually similar to the natural branching of rivers or lightning paths.
Used in graphics, artistic designs, and modeling branching systems.
Fractal Tree
Represents tree-like branching structures generated through recursive algorithms or L-systems.
Mimics the structure of natural trees, with each branch splitting into smaller branches that resemble the whole.
Demonstrates the efficiency of fractal geometry in resource distribution, like water or nutrients in trees.
Found in nature, architecture, and computer graphics.
❖ FRACTALS IN NATURE
Before delving into their most relevant use cases, it's crucial to understand how fractals function in nature. Fractals are are the blueprint for how nature organizes itself efficiently and adaptively. By repeating similar patterns at different scales, fractals enable natural systems to optimize resource distribution, maintain balance, and adapt to external forces.
Tree Branching:
Trees grow in a hierarchical branching structure, where the trunk splits into large branches, then into smaller ones, and so on. Each smaller branch resembles the larger structure. The angles and lengths follow fractal scaling laws, optimizing the tree's ability to capture sunlight and distribute nutrients efficiently.
Rivers and Tributaries:
River systems follow a branching fractal pattern, where smaller streams (tributaries) feed into larger rivers. This structure optimizes water flow and drainage, adhering to fractal principles where the system's smaller parts mirror the larger layout.
Lightning Strikes:
The branching paths of a lightning bolt are determined by the path of least resistance in the surrounding air. These paths are fractal because each smaller branch mirrors the larger discharge pattern, creating self-similar jagged structures which ensures efficient distribution of resources (electrical energy) across space.
Snowflakes:
Snowflakes grow by adding water molecules to their crystal structure in a symmetrical, self-similar pattern. The fractal nature arises because the growth process repeats itself at different scales, producing intricate designs that look similar at all levels of magnification.
Blood Vessels and Lungs:
The vascular system and lungs are highly fractal, with large arteries branching into smaller capillaries and bronchi splitting into alveoli. This maximizes surface area for nutrient delivery and oxygen exchange while maintaining efficient flow.
❖ FRACTALS IN MARKETS
Fractal Geometry provides a unique way to understand the seemingly chaotic behavior of financial markets. While price movements may appear random, beneath this surface lies a structured order defined by self-similar patterns that repeat across different timeframes.
Fractals reveal how smaller trends often replicate the behavior of larger ones, reflecting the nonlinear dynamics of market behavior. These recurring structures allow to uncover the hidden proportions that influence market movements.
Mandelbrot’s work underscores the non-linear nature of financial markets, where patterns repeat across scales, and price respects proportionality over time.
Fractals in Market Behavior: Mandelbrot argued that markets are not random but exhibit fractal structures—self-similar patterns that repeat across scales.
Power Laws and Scaling: He demonstrated that market movements follow power laws, meaning extreme events (large price movements) occur more frequently than predicted by standard Gaussian models.
Turbulence in Price Action: Mandelbrot highlighted how market fluctuations are inherently turbulent and governed by fractal geometry, which explains the clustering of volatility.
🔹 @fract's Version of Fractal Analysis
I've always used non-generic Fibonacci ratios on a logarithmic scale to align with actual fractal-based time scaling. By measuring the critical points of a significant cycle from history, Fibonacci ratios uncover the probabilistic fabric of price levels and project potential targets.
The integration of distance-based percentage metrics ensures that these levels remain proportional across exponential growth cycles.
Unlike standard ratios, the modified Fibonacci Channel extends into repeating patterns, ensuring it captures the full scope of market dynamics across time and price.
For example, the ratios i prefer follow a repetitive progression:
0, 0.236, 0.382, 0.618, 0.786, 1, (starts repeating) 1.236 , 1.382, 1.618, 1.786, 2, 2.236, and so on.
This progression aligns with fractal time-based scaling, allowing the Fibonacci Channel to measure market cycles with exceptional precision. The repetitive nature of these ratios reflects the self-similar and proportional characteristics of fractal structures, which are inherently present in financial markets.
Key reasons for the tool’s surprising accuracy include:
Time-Based Scaling: By incorporating repeating ratios, the Fibonacci Channel adapts to the temporal dynamics of market trends, mapping critical price levels that align with the natural flow of time and price.
Fractal Precision: The repetitive sequence mirrors the proportionality found in fractal systems, enabling to decode the recurring structure of market movements.
Enhanced Predictability: These ratios identify probabilistic price levels and turning points with a level of detail that generic retracement tools cannot achieve.
By aligning Fibonacci ratios with both trend angles and fractal time-based scaling, the Fibonacci Channel becomes a powerful predictive tool. It uncovers not just price levels but also the temporal rhythm of market movements, offering a method to navigate the interplay between chaos and hidden order. This unique blend of fractal geometry and repetitive scaling underscores the tool’s utility in accurately predicting market behavior.
$BTC1! Fib Simulation of Fractal (UPD)Perceiving the price action as a function of trading time justifies the quantitative approach in drawing geometric relationship between phases of cycles. Hence, it's safe for me to assume that market is a time fractal which has its own path regardless the collective opinions of the market participants. Logistic curve that reflects well the speed of information spreading made me ignore the voices of masses. The principle aligns with EMH - that the condition of the market is already reflected in the current price.
Impulsive and corrective waves are governed by golden rule in one way or the other. That's why I used fibonacci channels to build predictive models which reflect the interconnectedness of composite fractals to the whole cycle. By measuring the extreme levels of historic wave, the derived fibonacci channels exposed the timing, size and probability levels of the next ones.
In regular TA, people are wrongfully focused on covering their immediate expectations from the market, analyzing a narrow data range of the chart. Whereas, Fractal Analysis graphically shows how current price is interconnected with the entire history of fluctuations in a single probabilistic map.
In this update I fused earlier discovered structures and boundaries to the chart
Added more series of fib ratios derived from white triangle (src 0;1)
Linear boundaries of macro-fractal:
Implementation of fibs with big time Intervals:
As violet Fibs:
Other observations:
We're in a big triangle derived by linear extension 2021 tops and Full cycle (COVID - 2022 LOWS)
Source:
Implementation:
(On interactive chart it darkens till intersection)
Bottom to Bottom Circles : BTC Market Cycles Predictive Chart
BITCOIN Market Cycles: Predictive Chart
This chart showcases a unique visualization of the BITCOIN market's price evolution, incorporating hand-drawn circles that perfectly align with Bitcoin’s 4-year cycles. These circles act as pivotal zones, clearly indicating optimal moments to buy and sell.
Each circle represents an insurmountable boundary: as the price approaches the edge, it repeatedly collapses, marking key turning points in the market. This visual tool provides powerful insights for navigating the BITCOIN and altcoin space with precision.
QUALCOMM (QCOM): Diversified Growth Amid DowntrendQualcomm ( NASDAQ:QCOM ) presents an intriguing setup as we believe the wave I and a larger cycle might have concluded. Following its peak, NASDAQ:QCOM has dropped nearly 30%, retracing back to the range high. To finalize wave (A), we expect an additional leg down to complete the intra 5-wave structure. The likely target lies between $143 and $133, a range that aligns well with the Point of Control (POC) from March 2020 to now. This adds confluence to its significance as a potential support zone.
Despite the technical setup, we caution that the risk for a long position remains high. A more favorable entry could arise once NASDAQ:QCOM reclaims the range, validating the start of a potential bullish wave.
For the current quarter, Qualcomm projects revenues between $10.5 billion and $11.3 billion, with automotive sales anticipated to rise 50% year over year. CEO Cristiano Amon’s strategy to diversify Qualcomm beyond smartphones into chips for PCs, cars, and industrial machines underscores the company’s adaptability.
The next financial results release is scheduled for January 29, 2025, offering further insights into Qualcomm’s trajectory.
The $143-$133 range is a key zone for potential support, bolstered by its alignment with the POC. A decisive break below this zone could invalidate the bullish outlook, while a breakout above the range high may provide an opportunity to long this stock with lower risk. The completion of wave (A) would ideally coincide with a structural turnaround.
We are closely monitoring NASDAQ:QCOM for any signs of a reversal. Should the stock confirm a reclaim of the range, we may consider initiating a long position with a more precise stop-loss strategy. Until then, patience and vigilance are essential.