Why Does the Price Drop Every Time I Buy? Calculating the Growth Spiral of Memes from First Principles

Original Title: "Why Your Meme Coin Always Dumps? - Deconstructing the Meme Growth Spiral and Volume with First Principles"

Original Author: danny, Crypto Analyst

To most people, a Meme coin represents irrational exuberance, a casino of absurdity. But from a mathematical perspective, the birth of every thousandfold myth is not accidental. It is actually an application problem of middle school spatial geometry.

This article presents a disruptive viewpoint: the market cap of a Meme coin is not "pumped" but "supported" into existence. The value of a meme can be calculated!

We are accustomed to focusing on the Z-axis (price height) fluctuations, but we overlook that life and death are determined by the base radius constructed by X (narrative density) and Y (propagation nodes). A Meme with only height and no base is just an extremely thin "needle," easily tipped over by the wind; only an expanding consensus radius can, under the gravity of capital, support a stable, geometrically growing wealth cone.

Disclaimer: This article is an "Econophysics" popular science article, not a rigorous econometric paper, providing everyone with a brand-new perspective on memes.

1. The Beginning of Theory: The Three-Dimensional Coordinate System of Memes

In today's cryptocurrency market, Meme coins are often seen as irrational exuberance. But is it really so?

If we strip away the emotional noise, KOL shilling, and community hype, we will find that every emergence and demise of a phenomenal Meme follows a strict set of mathematical logic.

The essence of a Meme coin is the tokenization of attention economics. Its market cap is not determined by traditional discounted cash flows (DCF) but is collectively built by the breadth of narrative, community resonance, and the explosiveness of funds.

For better discussion, we define these factors as the XYZ three-dimensional growth spiral model.

These three axes are not just independent variables; they exhibit strong reflexivity - that is, a change in one variable will reinforce another variable, forming a positive feedback loop.

Now let's explain these parameters:

X-Axis: Narrative Density and Cultural Memes

Definition: The "genes" of a Meme. It includes core memes (such as Doge), origin stories (such as CZ's pet's name), cultural symbols (such as Pepe's Sad Frog), and the richness of community derivatives.

Key Metrics: Narrative Originality, Replicability, Emotional Resonance.

Y-Axis: Propagation Potential and Node Network

Definition: Information transmission pathway. From top nodes (CZ, Elon Musk) to mid-tier nodes (Alpha Callers, KOLs), down to end nodes (regular retail holders).

Key Metrics: Node Weight, Dissemination Coverage, Pump Frequency.

Z-Axis: Capital Flow and Liquidity Conduit

Definition: Monetization of attention. Includes on-chain capital flows, liquidity depth — i.e., embedded value or total sell-side depth.

Key Metrics: Market Cap, Trading Volume, Turnover Rate, and Liquidity (most critical).

2. XYZ Axis Interaction Growth Spiral Graph

If we were to plot these three axes in 3D space, a successful Meme Growth Trajectory typically follows an upward spiral trend: (see diagram below)

· Bottom (Start): X, Y, Z all close to zero.

· Ignition: Y-Axis spikes (KOL Pump), propelling Z-Axis (price) upwards. Trajectory tilts towards the Y-Z plane.

· Spin: Z-Axis growth attracts more Y (more discussion), Y triggers X's elaboration (richer content). Trajectory starts rotating around the X-Y-Z axes.

· Ascension: With X's upgrade (X'), the base of the cone expands (consensus widens), Z-Axis (market cap) reaches new heights.

· Failed Meme (Rug Pull): Typically seen as a Y-Axis surge, followed by a brief Z-Axis spike, but X-Axis fails to upgrade (lack of narrative), leading to a rapid collapse of Z-Axis back to zero, trace line forms an inverted V-shaped plunge.

3. Growth Curve Evolution: Spiral Ascension through Four Stages

From the previous section, we understand that a Meme's lifecycle is not linear but a vortex expanding around the Z-Axis (capital flow). In this section, we will analyze based on the four development stages of a Meme.

The following diagram illustrates its standard evolution path:

Phase One: The Ignition——X + Y → ΔZ

A powerful narrative (X) combined with a high-weight propagation node (Y), instantly igniting funds (Z).

Using Broccoli as an example:

· X (Narrative): On February 13, 2025, CZ announced his pet dog's name as "Broccoli." This is not just a simple pet name but carries deep metaphors of "CZ's comeback" and "BNB ecosystem resurgence," with "Broccoli" itself possessing a unique sound symbol and visual image (green = price increase).

· Y (Node): CZ himself as a top industry traffic node (Y-Max), with the propagation potential of a single tweet surpassing even that of a Super Bowl ad.

· Z (Outcome): Instant fund response. Hundreds of tokens with the same name quickly emerged on Solana and BNB Chain, with the market cap of a top token surpassing $1.5 billion within hours, and early snipers making millions in profits within 20 minutes.

The growth of the Z-axis in this phase is pulsatile, entirely dependent on the single-point outbreak of the Y-axis.

Phase Two: Reflexivity Establishment (The Reflexivity Loop)——Z↑→ Y↑

Price (Z) itself becomes the best advertising and propagation channel (Y). When the Z-axis (market value) rises rapidly, creating a "hundredfold golden dog" wealth effect, it will have a reverse impact on the Y-axis.

· Passive Propagation: KOLs who originally ignored the meme start actively mentioning it to ride the trend (capturing traffic).

· FOMO Spread: The Top Gainers list itself is the most potent propagation node. Media reports (like "an address profits $6 million") further expand the reach.

· BNB Chain Strategy: The BNB Chain officially injects energy into the Z-axis through a "Meme Innovation Contest" and a "Daily Airdrop" plan (airdropping golden dogs worth 33 BNB to the community daily), artificially maintaining the vitality of the Y-axis.

Phase Three: Narrative Upgrade and Solidification (Narrative Upgrade) — Y_expansion → X'

The expanded network effect (Y) forces the narrative (X) to undergo a secondary iteration (X'). Relying solely on the "CZ's Dog" meme (X) is insufficient to sustain long-term market value. When the Y-axis expands to hundreds of thousands of holder addresses, the community spontaneously begins creating new narratives (X').

From "Meme" to "Culture": The community starts creating memes, establishing the "Broccoli Cult," imbuing the token with a certain spiritual significance (e.g., "Anti-VC Coin," "Symbol of BNB Chain Revival").

Narrative Instrumentalization: For example, FLOKI evolved from a simple meme to an ecosystem with the Valhalla game and DeFi protocols. This is also a form of X → X' upgrade.

Phase Four: The Value Black Hole — X'→ Z_max

The upgraded narrative (X') can carry a larger scale of funds (Z).

When the X-axis completes the upgrade from "Meme" to "Totem," the upper limit of the Z-axis is unlocked.

Change in Fund Nature: From early "fast in, fast out" smart money to "diamond hand" community funds and institutional funds attempting to allocate.

Infrastructure Vampirism: At this point, the meme is no longer just a customer acquisition tool; it begins to feed back into on-chain infrastructure. Massive trading volume brings a significant amount of BNB burn and fee income to the BNB Chain, while also providing liquidity entry points for other applications in the ecosystem (such as Aster derivatives trading, Pancake's volume).

4. A Conjecture Triggered by a Cone Formula?

If you are observant, you may notice that the three-dimensional graph above looks somewhat like a cone. Is it possible that we can apply the volume formula of this cone

V = ⅓ * Base Area * Height into the growth model of a Meme coin

4.1. Variable Mapping: Building a Growth Model

We will map the various geometric elements of the cone to the variables x, y, z you proposed:

Base Radius r = x * y: Boundary of social consensus

· x (Content/Narrative): This is the "gene" of a Meme. Good content determines the virality of consensus.

· y (Propagation Nodes): These are the community, KOLs, and hodler addresses. Nodes determine the reach of the narrative.

· r (Radius): Represents the physical boundary of consensus. A larger radius means more people know and are willing to believe in the story, leading to a more stable foundation.

· Height h = z (Capital/Sentiment Leverage): The speed and density of capital inflow determine the vertical height of price appreciation.

· Volume V = Market Cap: The resulting scale of market capitalization.

4.1.1 Why is the relationship between radius x * y squared?

In the world of Memes, the combination of narrative and nodes exhibits network effects.

If content x is just mediocre imitation, even with many nodes y, the radius r is hard to expand.

When a highly penetrating narrative (x) meets highly interactive propagation nodes (y), the consensus surface area expands exponentially. The squared term in the formula implies that as the underlying community consensus expands slightly, the potential supported volume (market cap) grows exponentially.

4.1.2 Why is capital z a linear height?

Capital z determines how high the price pumps. However, in the Meme model, without the underlying surface area (x and y) supporting the capital height, it is unstable. If there is only z (whale entry for a pump) without r (widespread retail consensus), the cone will become an extremely thin "needle" that collapses at the slightest breeze.

True blue-chip Memes (like DOGE, PEPE) have a huge base diameter, allowing the overall volume to remain substantial even if the capital height h fluctuates.

4.1.3 The Allure of the 1/3 Coefficient: Meme Erosion and Attention Decay

Scientists have found that the volume of a cone is only one-third that of a cylinder with the same base and height. In the Meme market, this represents the frictional loss of attention, although 1/3 is an assumed value and could actually be 1/300.

Not everyone who hears the narrative will buy in. Not all incoming capital can translate into long-term held market value. This coefficient reminds us that a Meme's market cap can never fully cover the attention flow it reaches, with a significant amount of bubble evaporation and attention diversion.

4.2 Trajectory Analysis: From "Point" to "Cone"

The upward trajectory of a Meme coin usually follows the generation process of a cone:

· Sprout: Narrative x has just come into being, node y is extremely few, and funding z is just starting to be injected. At this point, the volume is negligible.

· Rooting Downward: As more node y join, narrative x begins to proliferate. At this stage, the most important thing is not the price (height), but increasing the number of holding addresses and community activity (expanding radius r).

· Vertical Eruption: When the consensus base is large enough, the influx of funding z will create an astonishing leverage effect. Since the base radius has solidified, increasing the same z will cause the volume V to rapidly expand.

A successful Meme coin trajectory is essentially about expanding the base first, then increasing the height.

5. Volume Formula of Cone: Boundaries and Limitations

5.1 Defining the States of "Healthy" and "Malformed" Growth

This model sets r (narrative × node) as a square term and sets z (funding) as a linear term. There are two main, fairly obvious effects:

· Capturing Network Effects: In the Meme field, a 10x narrative spread (r) often can support a 100x market cap (V) growth. This explains why some coins, even if the funding amount (h) has not reached a tipping point, as long as the community foundation (r) is thick enough, its valuation potential will experience a geometric leap.

· Explaining the Physical Structure of "Collapse": If a project's radius r (consensus) is shrinking, even if you pour in a lot more funding z to pump the price, the volume of the cone will rapidly shrink due to the collapse of the base.

In addition, through this geometric model, we can easily distinguish two typical failure models:

· "Bar" Model (high z, very low r): Only whales wash trading or pump the price, lacking community discussion and narrative consensus. This kind of cone is extremely unstable, and once the funding z is withdrawn, the volume instantly drops to zero.

· "Flat Pancake" Model (large r, very low z): The community is very lively, the narrative is good, but there is simply no funding coming in. This kind of cone only has area but no volume, representing a "all bark and no bite" poor community.

5.2 Limitations

In the real-world secondary market application, there are several important "physical deformations" to note:

· Coupling between variables: In the formula, r and h are independent variables, but in the Meme market, an increase in z (funds) will in turn strengthen x (narrative) and y (propagation nodes). This is the famous "bulls are on steroids" effect. The higher the price, the more the narrative resembles truth, and the faster the node diffusion.

· Dynamic nature of the ⅓ coefficient: In an extremely crazy bull market, this coefficient may approach 1 (become a cylinder) as emotions smooth out all losses; whereas in a bear market, this coefficient may become 1/1000, meaning the vast majority of attention cannot be converted into purchasing power.

· Lack of a time dimension: A cone is a static geometric shape, but Meme is time-sensitive. Introducing a "decay rate" would make this model more perfect, as the narrative x of a Meme will naturally shrink with aesthetic fatigue.

6. Broccoli Case Study

6.1. Elements of Broccoli

· x (Content/Narrative): "CZ Personally Certified" — This is top-tier narrative and influence.

· y (Propagation Nodes): CZ's tens of millions of fans, BNB Chain official account, Four.Meme platform, and the lurking "scientists" and PVP players across the entire network.

· z (Funds/Market Value): Funds held on the BNB chain and "hot money" brought in from other chains through cross-chain transactions.

6.2. Four-Stage Trajectory Reconstruction

Stage One: Bottom (Start) — Fog Phase

February 13, 2025, CZ teases the upcoming reveal. x, y, z are almost zero, but the market is full of "static electricity." The entire network begins to speculate on the name, leading to a plethora of tiny misdirected cones like BNBDog, CZDoge, and so on.

Stage Two: Ignition (Launch) — Narrative Nuclear Explosion

CZ tweets, officially announcing the dog's name as Broccoli with an accompanying image. The y-axis (nodes) instantly max out. Twitter, Telegram channels almost instantaneously propagate in sync on a second-by-second basis.

Due to the narrative x being directly provided by CZ, authenticity is confirmed. Funds z poured in wildly, and hundreds to thousands of tokens with the same name instantly emerged on platforms like Four.Meme. The trajectory line at this moment exhibited an almost vertical incline in the y-z plane.

Phase Three: Spin — Jungle Combat (PVP)

Within 2-12 hours after the reveal, thousands upon thousands of Broccolis appeared in the market. To compete for the "true identity," various communities began frenzied derivative creations (x's competition). At this point, the model is in a spinning state. Some tokens rely on community-driven buy pressure to increase z, while others enrich x with more entertaining memes.

Only those Broccolis that can continuously stimulate y (more node discussions) and enrich x (narrative upgrades, such as charity work or gaming) can maintain the spin. The rest, due to a lack of x, lose their spinning power and directly enter the collapse process.

Phase Four: Ascension — Consensus Settling

In the end, only 1-2 "chosen ones" stand out, gaining attention from the BNB Foundation or recognition from mainstream trading platforms.

By this time, the base area r = x * y has solidified due to extensive community building. The narrative has ascended from "CZ's pet" to "BNB Chain's mascot." Even if fund z experiences occasional fluctuations, the market value cone remains towering due to its extremely stable base.

6.3 Warning: Ascended Broccolis

In the brawl of 2025, 99.99% of Broccolis plummeted in an "inverted V-shaped" fall.

During the launch period, they relied on counterfeiting or internal pumps to raise the z-axis significantly. The Dev team was purely focused on harvesting, with no intention of managing x (content) and y (genuine community nodes). Therefore, this cone was an extremely thin "needle," and after reaching the peak of the z-axis, due to the base radius r approaching zero, it instantly lost balance, and the trajectory line plummeted vertically, leaving a mess behind.

CZ's Broccoli case proved: The ultimate battle of Meme coins is not about who mints first (z) but about who can expand the "CZ's pet" point (x) into the largest circle (r) through community power (y).

Broccoli was perhaps the largest "same-base-area cone speed competition" on Meme in 2025. Under the same x narrative, tens of thousands of projects competed in y and z, ultimately proving that only "narrative upgrades + node stickiness" can lead to a breakthrough in market value.

7. Case Study of Pnut

Pnut's Three-Dimensional Coordinate Breakdown

· X Axis (Narrative Density - Emotion and Justice): This is not just a squirrel meme; it carries the narratives of "resisting government overreach" and "seeking vengeance for innocent life." From "a cute squirrel → a hero killed by the establishment → a political totem of the MAGA movement." Its narrative density has remarkably achieved cross-border, cross-class resonance in meme history.

· Y Axis (Dissemination Node - Dimensionality Reduction Strike): Top node Y_max: Elon Musk continuously tweeted, followed by other top influencers like Joe Rogan. These nodes are not just "pumping KOLs" but giant nodes with the ability to set social agendas.

· Z Axis (Funds Conduit - Emotional Leverage): With lightning-fast liquidity on the Solana chain, coupled with rapid listing on top CEXs like Binance, funds z flowed in rapidly.

Phase 1. Ignition Phase: Injection of Tragic Narrative Genes

x (Justice/Vengeance) formed instantly, y (local community) began to spread. The trajectory bounced vertically from the origin. The action of the New York Environmental Protection Agency injected a highly penetrating x gene into Pnut. At this time, z (funds) were still languishing on-chain, but the energy at the bottom had begun to accumulate.

Phase 2. Spiral Phase: "Gravity Pull" of Top Nodes

The Y-axis experienced a magnitude jump due to Musk's (Elon Musk) intervention (Y → Y_max).

The skyrocketing price z attracted the attention of the entire network. As Elon's tweets had strong self-referentiality, for every doubling of the price, more traditional media and political KOLs (new nodes) joined the discussion. The trajectory line began to rotate vigorously in three-dimensional space, and the radius r expanded rapidly.

Phase 3. Dimensional Upshift: From "Squirrel" to "Political Totem"

The X-axis completed the upshift (from "animal protection" to "US election/resisting the establishment"). This is Pnut's most solid step. Due to the upgrade of narrative x, the circular base area r = x*y is no longer limited to the crypto community. At this stage, Pnut is no longer a local meme but a cultural asset. Even if funds z experience a phase-wise pullback, the huge consensus base can still withstand selling pressure.

Phase 4. Value Black Hole: The Collapse and Reconstruction of Blue-Chip Consensus

Listed on top exchanges such as Binance, with funds soaring to new heights. A massive V (Market Cap) has been formed. It begins to absorb liquidity within the Solana ecosystem like a black hole. At this point, the Pnut cone has fully solidified, becoming the object that all subsequent animal-type Memes attempt to imitate.

A Final Note

After reading so much theoretical analysis, you ask me as an ordinary user, how should I identify, participate in, and embrace meme opportunities on the BNB Chain, Solana, Base, and Xlayer? How can I seize a great opportunity and achieve great results?

To be continued in the next breakdown.

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