Now that so much of collective action takes place online, web-generated data can further understanding of the mechanics of Internet-based mobilisation. This trace data offers social science researchers the potential for new forms of analysis, using real-time transactional data based on entire populations, rather than sample-based surveys of what people think they did or might do. This paper uses a `big data' approach to track the growth of over 8,000 petitions to the UK Government on the No. 10 Downing Street website for two years, analysing the rate of growth per day and testing the hypothesis that the distribution of daily change will be leptokurtic (rather than normal) as previous research on agenda setting would suggest. This hypothesis is confirmed, suggesting that Internet-based mobilisation is characterized by tipping points (or punctuated equilibria) and explaining some of the volatility in online collective action. We find also that most successful petitions grow quickly and that the number of signatures a petition receives on its first day is a significant factor in explaining the overall number of signatures a petition receives during its lifetime. These findings have implications for the strategies of those initiating petitions and the design of web sites with the aim of maximising citizen engagement with policy issues.