---
# System prepended metadata

title: 'Metric expansion of cyberspace:'

---

# Metric expansion of cyberspace:

As the concept of metric expansion of space in cosmology describes the increasing distance between distant galaxies over time due to the expansion of the universe, it can be represented by the following equation:

```
d = H * z
```

Where:
- `d` = the comoving distance between two galaxies
- `H` = the Hubble constant
- `z` = the redshift

Similarly, the growth and expansion of intelligent contract accumulators and AMM networks of DEXES over time can be represented by the following equations:

**Compound interest formula:**
```
A = P * (1 + r/n)^(nt)
```

Where:
- `A` = the final amount of data or the size of the network
- `P` = the initial amount of data or the size of the network
- `r` = the growth rate or the rate of new smart contract logics being created
- `n` = the number of times the data or network size is compounded per time period
- `t` = the time period

**Exponential growth formula:**
```
y = a * e^(rt)
```

Where:
- `y` = the final quantity of data or the size of the network
- `a` = the initial quantity of data or the size of the network
- `e` = Euler's number (approximately equal to 2.718)
- `r` = the growth rate or the rate of new smart contract logics being created
- `t` = the time period

Together, these equations demonstrate how the continuous creation and evolution of smart contract logics, the accumulation of data, and the expansion of the network drives an arrow of time in the world of blockchain and decentralized finance, much like the metric expansion of space creates an arrow of time in cosmology.

