Why do the memes you buy only depreciate? — Deconstructing the growth spiral and volume of memes using first principles

Author: danny

To most people, Memecoin is an irrational frenzy, a gambling game of the greater fool theory. But from a mathematical perspective, the birth of every 10,000x myth is not accidental; it is actually a middle school spatial geometry application problem.

This article presents a disruptive perspective: Meme's market capitalization wasn't "increased," but rather "inflated." Meme's value can be calculated!

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

Note: This article is a popular science article on "financial physics" rather than a rigorous econometrics paper, and is intended to give you a fresh perspective on memes.

1. The Beginning of the Theory: The Three-Dimensional Coordinate System of a Meme

In the current cryptocurrency market, Meme Coin is often seen as part of an irrational frenzy. But is that really the case?

If we strip away emotional noise, KOL endorsements, and community hype, we'll find that the birth and demise of every phenomenal meme follows a rigorous mathematical logic.

The essence of Meme Coin is the tokenization of the attention economy. Its market value is not determined by the traditional discounted cash flow (DCF), but by the breadth of the narrative, the resonance of the community, and the explosive power of funds.

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

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

Let's explain these parameters:

X-axis: Narrative density and cultural memes

Definition: The "genes" of a meme. This includes core memes (such as Doge), origin stories (such as CZ's pet name), cultural symbols (such as Pepe's sad frog), and the richness of community-created content.

Key metrics: narrative originality, replicability, and emotional resonance.

Y-axis: Propagation potential and node network

Definition: The information transmission pipeline. From the top-level node (CZ, Elon Musk) to the secondary nodes (Alpha Callers, KOLs), and then to the end nodes (ordinary retail investors).

Key metrics: node weight, propagation coverage, and frequency of order placement.

Z-axis: Fund flow and liquidity carrier

Definition: The monetization of attention. This includes on-chain fund inflows and liquidity depth—that is, the value held or the total amount of sell orders that can be absorbed.

Key metrics: market capitalization, trading volume, turnover rate, and liquidity (the most important metric).

2. Graph illustrating the growth curve of the interaction between the XYZ axes

If we plot these three axes in three-dimensional space, a successful meme growth trajectory will generally show a spiral upward trend: (as shown in the figure below)

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

Ignition: A sudden surge in the Y-axis (KOL's trading recommendation) drives a jump in the Z-axis (price). The trajectory line slopes towards the YZ plane.

Spin: Growth along the Z-axis attracts more Y (more discussion), and Y inspires further creation in X (richer content). The trajectory line begins to rotate around the XYZ axes.

Ascension: As X is upgraded (X'), the base area of the cone expands (the consensus range becomes wider), and the Z-axis (market capitalization) reaches a new height.

A failed meme (Rug Pull): This usually manifests as a burst on the Y-axis followed by a brief rise on the Z-axis, but the X-axis fails to follow suit (lack of narrative), causing the Z-axis to collapse rapidly to zero, with the trajectory line falling in an inverted V-shape.

3. Evolution of the growth curve: a spiral ascent in four stages.

As we learned in the previous section, the lifecycle of a meme is not linear, but rather a vortex that expands continuously around the Z-axis (the flow of funds). In this section, we will analyze the meme based on its four development stages.

The image below shows its standard evolutionary path: (I was stunned too, the AI drew it so cool?! 🤣)

(Note: For ease of reading and comprehension, I will not write it in paragraphs.)

Phase 1: Ignition — X + Y → ΔZ

A powerful narrative (X) combined with a high-weight dissemination node (Y) instantly triggers a surge in funding (Z).

Take Broccoli as an example:

X (Narrative): On February 13, 2025, CZ announced that his pet dog's name was "Broccoli". This is not just a simple pet name, but also carries a deeper metaphor of "CZ's comeback" and "BNB's ecological return". Moreover, "Broccoli" itself has a unique sound symbol and visual image (green = rise).

Y (Node): CZ himself is a top traffic node in the industry (Y-Max), and the spread potential of a single tweet from him even exceeds that of a Super Bowl ad.

Z (Result): Instantaneous capital response. Hundreds of tokens with the same name quickly emerged on Solana and BNB Chain, with the top token's market capitalization exceeding $1.5 billion within hours, and early adopters making millions in 20 minutes.

During this stage, the growth of the Z-axis is pulse-like, entirely dependent on the single-point burst of the Y-axis.

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

Price (Z) itself becomes the best advertising and communication channel (Y).

When the Z-axis (market capitalization) rises rapidly, creating a "hundred-fold golden dog" wealth effect, it will have a reverse effect on the Y-axis.

Passive spread: KOLs who were not originally interested in the meme started mentioning it in order to gain popularity (traffic capture).

FOMO spreads: Top Gainers lists are themselves the most powerful dissemination nodes. Media reports (such as "an address made $6 million in profit") further expand the dissemination radius.

BNB Chain's strategy: BNB Chain officially injects energy into the Z-axis through the "Meme Innovation Competition" and the "Daily Airdrop" program (purchasing 33 BNB "golden dogs" and airdropping them to the community every day) in order to maintain the activity of the Y-axis.

Phase Three: Narrative Upgrade and Solidification – Y_expansion → X'

The expanded dissemination network (Y) forces the narrative (X) to undergo a second iteration (X').

Relying solely on the "CZ's dog" meme (X) cannot sustain a long-term market capitalization. As the Y-axis expands to hundreds of thousands of holding addresses, the community begins to spontaneously create new narratives (X').

From "memes" to "culture": The community started creating memes, establishing a "broccoli cult", and giving the token a certain spiritual meaning (such as "resisting VC coins" and "a symbol of the revival of BNB Chain").

Instrumental narrative: such as FLOKI evolving from a simple meme into an ecosystem with Valhalla games and DeFi protocols. This is also an upgrade from X to X'.

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

The upgraded narrative (X') can support a larger amount of funding (Z).

Once the X-axis has been upgraded from a "local dog" to a "totem", the upper limit of the Z-axis has been unlocked.

The nature of the funds has changed: from early "quick in and quick out" smart money to "diamond hand" community funds and institutional funds attempting to allocate assets.

Infrastructure Suckering: At this point, the meme is no longer just a customer acquisition tool; it begins to feed back into the on-chain infrastructure. The massive transaction volume brings BNB Chain a large amount of BNB burning and transaction fee revenue, while also providing liquidity entry points for other applications within the ecosystem (such as Aster derivatives trading and Pancake trading volume).

4. A conjecture sparked by a formula for a cone?

If you're observant, you might notice that the 3D diagram above resembles a cone. Is it possible that we can find the volume formula for this cone?

The formula V = ⅓ * base area * height is applied to the growth model of Meme coin.

4.1. Variable Mapping: Building a Growth Model

We 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 contagiousness of consensus.

y (propagation nodes): These are the community, KOLs, and token holder addresses. Nodes determine the coverage of the narrative.

r (radius): Represents the physical boundary of consensus. The larger the radius, the more people know and are willing to believe the story, and the more stable the foundation.

h = z (capital/sentiment leverage): The speed and density of capital inflows determine the vertical height of price increases.

Volume V = Market Cap: The final market capitalization.

4.1.1 Why is the radius x * y a quadratic relationship?

In the world of memes, the combination of narrative and nodes creates a network effect.

If the content x is just a mediocre imitation, even if there are many nodes y, the radius r will be difficult to expand.

When a highly persuasive narrative (x) encounters a frequently interacting propagation node (y), the consensus area expands exponentially. The squared term in the formula means that if the underlying community consensus expands even slightly, the potential volume (market capitalization) it supports will increase exponentially.

4.1.2 Why is the funding z linear in height?

The amount of capital z determines how high the price can go. However, in the Meme model, the height of capital without the support of a base area (x and y) is unstable.

If there is only z (whales entering the market to pump up prices) but no r (broad consensus among retail investors), the cone will become an extremely thin "needle" that will collapse at the slightest breeze.

True blue-chip memes (such as DOGE and PEPE) have huge base diameters, which makes their overall size still enormous even with high capital fluctuations.

4.1.3 The allure of coefficient ⅓: Meme depletion and attention decay

Scientists have discovered that a cone's volume is only one-third that of a cylinder with the same base and height. In the meme market, this represents a frictional loss of attention, but ⅓ is an assumed value; in reality, it might be 1/300.

Not everyone who hears the story will buy it.

Not every investment can be converted into long-term holding value.

This coefficient reminds us that the market value of a meme can never fully cover the attention it receives, as there is a significant amount of bubble evaporation and attention shift.

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

The upward trajectory of Meme coin typically follows a cone-shaped formation process:

Infancy: Narrative x has just been born, nodes y are extremely few, and funds z have just begun to be injected. At this stage, its volume is negligible.

Rooting downwards: As more nodes y join, the narrative x begins to fission. The most important aspect at this stage is not price (height), but rather increasing the number of holding addresses and community activity (expanding the radius r).

Vertical eruption: When the consensus base is large enough, the inflow of funds z will generate a tremendous leverage effect. Since the base radius is already fixed, increasing z by the same amount will cause the volume V to expand rapidly.

A successful Meme coin trajectory essentially involves first expanding the base and then increasing the height.

5. Boundaries and limitations of the formula for the volume of a cone

5.1 Define “healthy” and “deformed” growth states

This model sets r (narrative × nodes) as a quadratic term and z (funds) as a linear term. This has two main advantages:

The network effect has been captured: In the meme space, a 10x narrative spread (r) can often support a 100x increase in market capitalization (V). This explains why some coins, even if their capital (h) hasn't reached its tipping point, can experience exponential valuation growth as long as their community base (r) is strong enough.

The physical structure of a "crash" is explained: If the radius r (consensus) of a project is shrinking, even if you invest more funds z to pump the price, the volume of the cone will shrink rapidly due to the collapse of the bottom.

Furthermore, this geometric model allows us to easily distinguish two typical failed models:

The "telephone pole" model (high z, extremely low r): Only large investors engage in wash trading or Ponzi schemes manipulate the price, lacking community discussion and narrative resonance. This cone-shaped structure is extremely unstable; once the funds (z) are withdrawn, its volume instantly drops to zero.

The "Big Pancake" Model (large r, very low z): The community is very lively, and the narrative is good, but there's a lack of funding. This cone-shaped structure has area but no volume, representing a poor community that's "praised but not popular."

5.2 Limitations

In real-world applications in the secondary market, the following "physical variations" require attention:

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 "price surge effect." The higher the price, the more the narrative resembles the truth, and the faster the nodes spread.

The dynamics of the coefficient: In an extremely bullish market, this coefficient may approach 1 (becoming a cylinder) because emotions smooth out all losses; while in a bear market, this coefficient may become 1/1000, meaning that most attention cannot be converted into purchasing power.

The lack of a time dimension: A cone is a static geometric shape, but a meme has a time limit. Introducing a "decay rate" would make this model more perfect, because the narrative of a meme will naturally shrink as aesthetic fatigue sets in.

6. Broccoli Case Study

6.1. Elements of Broccoli

x (Content/Narrative): “CZ personally vouched for it” — This is top-tier narrative and influence.

y (propagation nodes): CZ's millions of fans, BNB Chain's official account, the Four.Meme platform, and "scientists" and PVP players lurking across the internet.

z (funds/market capitalization): Existing funds on the BNB chain, as well as "hot money" coming from other chains.

6.2. Four-stage trajectory reconstruction

Phase 1: The Bottom (Start) – The Fog Period

Before CZ's announcement on February 13, 2025, x, y, and z were almost zero, but the market was filled with "static electricity." The entire internet began speculating about the name, resulting in numerous tiny cones pointing in the wrong direction, such as BNBDog and CZDoge.

Phase Two: Ignition – Narrative Explosion

CZ tweeted, officially announcing the dog's name as Broccoli and posting a picture. The y-axis (node) surged instantly. The news spread almost simultaneously on Twitter and Telegram channels within seconds.

Since x (the narrative) is directly provided by CZ, its authenticity is confirmed. Funds z poured in frantically, with hundreds or even thousands of tokens of the same name being generated instantly on platforms like Four.Meme. At this moment, the trajectory line shows an almost vertical tilt in the yz plane.

Phase Three: Spin – Jungle Melee (PVP)

Within 2-12 hours of the name being revealed, thousands of Broccoli instances appeared on the market. Various communities began a frenzy of fan-made creations (a competition among x instances) in the quest to claim the "real" Broccoli.

The model is currently in a rotating state. Some tokens increase z through spontaneous community purchases, while others enrich x through more interesting meme graphs.

Only those Broccoli that can continuously stimulate y (more node discussion) and enrich x (narrative upgrade, such as doing charity or making games) can maintain rotation; the rest, due to the lack of x, lose their rotational force and directly enter the collapse process.

Phase Four: Ascension – Consensus Building

Ultimately, only 1-2 "chosen ones" will emerge and gain the attention of the BNB Foundation or the recognition of mainstream exchanges.

At this point, the base area r = x * y has become solidified due to long-term community building. The narrative has evolved from "CZ's dog" to "BNB Chain's mascot." Even if the funds z fluctuate occasionally, the cone of market capitalization remains standing due to the extremely stable foundation.

6.3 Warning: Sublimated Broccoli

In the chaotic battle of 2025, 99.99% of Broccoli fell in an "inverted V" shape.

During their initial launch phase, they artificially inflated their z-axis significantly through deception or internal manipulation. Devs were purely focused on profiting and had no intention of cultivating x (content) or y (real community nodes). Therefore, this cone-shaped structure is like an extremely thin needle. After reaching its peak on the z-axis, due to the base radius r approaching zero, it instantly lost its balance, and its trajectory plummeted vertically, leaving behind a mess.

CZ's Broccoli case proves that the ultimate battle for Meme coins is not about who issues their coins first (z), but about who can use the power of the community (y) to expand the "CZ's pet" point (x) into the largest possible circle (r).

Broccoli: This should be the largest "same-base-area cone speed race" on Meme 2025. Under the same x narrative, tens of thousands of projects are competing for y and z, ultimately proving that only "narrative upgrade + node stickiness" can achieve a breakthrough in market value.

7. Pnut Case Study

Pnut's 3D coordinate decomposition

X-axis (Narrative Density - Emotion and Justice): This is not just a squirrel meme; it embodies narratives of "resisting the excessive expansion of public power" and "avenging innocent lives." From "a cute squirrel → a hero killed by the system → a political totem of the MAGA movement," its narrative density achieves a rare cross-border and cross-class resonance in meme history.

Y-axis (propagation nodes - dimensional reduction attack): Top-level node Y_max: Elon Musk tweeted continuously, followed by top influencers like Joe Rogan. This type of node is not simply a "marketing KOL," but a giant node with the ability to set the social agenda.

Z-axis (Capital Carrier - Emotional Leverage): The extremely fast liquidity on the Solana chain, coupled with the lightning-fast listing of top CEXs such as Binance, causes funds to flow in rapidly.

Phase 1. Ignition Period: The Injection of Tragic Narrative Genes

x (justice/revenge) is formed instantly, and y (local community) begins to spread.

The trajectory bounces vertically upwards from the origin. The New York Environmental Protection Agency's actions have injected Pnut with a highly penetrating x-gene. At this time, z (funds) is still sluggish on the chain, but the energy at the bottom has begun to accumulate.

Phase 2. The Hesitation Period: The "Gravity Pull" of the Top-Level Node

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

The surge in price z attracted widespread attention online. Due to the highly reflexive nature of Elon's tweets, each doubling of the price drew in more traditional media and political KOLs (new nodes) to the discussion. The trajectory line began to rotate violently in three-dimensional space, and its radius r rapidly expanded.

Phase 3. The Ascension Phase: From "Squirrel" to "Political Totem"

The X-axis has been upgraded (from "animal protection" to "US election/resistance to the system").

This is Pnut's most solid step. Because of the upgraded narrative x, the base area r = x*y of the cone is no longer limited to the crypto world. At this stage, Pnut is no longer just a monstrosity, but a cultural asset. Even if there's a temporary pullback in funds z, the massive consensus base can withstand selling pressure.

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

Listed on top exchanges like Binance, funds reached their peak.

A massive V-shaped market capitalization had formed. It began to absorb liquidity within the Solana ecosystem like a black hole. At this point, Pnut's cone had fully hardened, becoming the model that all subsequent animal-themed memes attempted to emulate.

In conclusion

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

To find out what happens next, please stay tuned for the next episode.