---
title: "Relationship between the flagship server and others over time"
resource-path:
  - "../"
---

## Competition Among Servers in Attracting Newcomers

_How does mastodon.social factor into the aggregate Mastodon onboarding process?_

![](images/mastodon-social-signups-2020-11-01.png){fig-env="figure" width=6cm height=6cm}

: The main page of mastodon.social as viewed by a logged out web browser on November 1, 2020. The sign-up form is blurred out and instead there is a message suggesting to either sign up on mastodon.online or see a list of servers accepting new accounts at joinmastodon.org.

Throughout its history, Mastodon's flagship server, mastodon.social, has allowed and disallowed open sign-ups at various times. When the website did not allow sign-ups, it displayed a message redirecting those interested in signing up for an account to mastodon.social or alternatively to a list of potential servers at joinmastodon.com.

We found three main periods during which mastodon.social did not accept new signups by first noting the times where the proportion of new accounts on mastodon.social drops to zero. We then used the Internet Archive to verify that signups were disabled during these periods.

1. An extended period of through the end of October 2020.

2. A temporary issue when the email host limited the server in mid-2022.

3. Two periods in late 2022 and early 2023.

We construct an interrupted time series using an autoregressive integrated moving average (ARIMA) model for sign-ups on mastodon.social, the servers linked in joinmastodon.org, and all other servers. For the first period, we also include mastodon.online since mastodon.social linked to it directly during that time.

$$
\begin{aligned}
y_t &= \beta_0 + \beta_1 \text{open}_t + \beta_2 \text{day}_t + \beta_3 (\text{open} \times \text{day})_t \\
&\quad + \beta_4 \sin\left(\frac{2\pi t}{7}\right) + \beta_5 \cos\left(\frac{2\pi t}{7}\right) \\
&\quad + \beta_6 \sin\left(\frac{4\pi t}{7}\right) + \beta_7 \cos\left(\frac{4\pi t}{7}\right) \\
&\quad + \phi_1 y_{t-1} + \phi_2 y_{t-2} + \epsilon_t
\end{aligned}
$$

where $y_t$ is the number of new accounts on a server at time $t$, $\text{open}_t$ is a binary variable indicating if the server is open to new sign-ups, $\text{day}_t$ is an increasing integer represnting the date, and $\epsilon_t$ is a white noise error term. We use the sine and cosine terms to account for weekly seasonality.


| Period     | Setting | Significant |
|------------|:----------------|:----|
| 2020-2021  | mastodon.online | Yes |
|            | JoinMastodon    | No  |
|            | Other           | No  |
| Mid 2022   | JoinMastodon    | No  |
|            | Other           | No  |
| Early 2022 | JoinMastodon    | No  |
|            | Other           | No  |

: Results from ARIMA models for the number of new accounts on mastodon.social, mastodon.online, servers linked in joinmastodon.org, and all other servers.

# Appendix {#appendix .appendix}

## Push and Pull Model

{{< include _push_pull.qmd >}}