Fossil-fuel use may look like a chaotic rise and fall. But this study finds that it carries a remarkably strong memory: what happened before can help shape what happens next. Fossil fuels remain a critical energy resource supporting the development of the global economy, and fossil energy still accounts for more than 80% of global disposable energy consumption.

But the fuel mix has changed over time: reliance moved from simple coal toward a combination of oil and natural gas, while coal consumption is declining and oil and gas are still multiplying. The findings suggest that fossil fuel consumption has predictable long-term patterns, making this history useful when assessing future energy demands.

To make consumption patterns visible, the study uses the visibility graph method to convert time series into complex networks, allowing those patterns to be analyzed further. The coal, oil, and natural-gas consumption data all have values greater than zero point five, rather than behaving like fully random sequences.

Most fossil-fuel consumption values exceed zero point nine, indicating long-term memory: the past continues to influence the future over long stretches. Global fossil-fuel use rose over the period shown, with coal, oil, and gas all reaching much higher levels than at the start.

The sharp drop in twenty-twenty stands out as a brief interruption to that long upward movement. The study examines fossil-fuel consumption in 38 countries to assess global trends and differences. It reports that the visibility-graph approach uncovers distinct features of coal, oil, and gas consumption when they are viewed as networks rather than only as sequences of yearly totals.

The global picture shifts sharply alongside economic growth: Venezuela moves from the world’s leading fossil-fuel consumer in 1968 to almost none, while China rises from near the bottom to the top by 2020. Because coal, oil, and gas consumption in these countries are long-term memory time series, looking only at the original consumption data cannot discover every feature in them.

The added measure reveals new characteristics, including fuel-consumption differences between different countries and within the same country. The analysis finds that all fossil-fuel consumption data in these countries exhibit long-term memory characteristics, indicating a significant relationship between fossil-fuel consumption and economic development.

The Hurst index analysis finds long-term memory across fossil fuel consumption data from 38 countries, indicating a significant relationship between fossil fuel consumption and economic development. Across the countries examined, fossil-fuel consumption follows persistent long-term patterns, while a second view reveals differences between countries and between fuels.

That could improve energy planning and resource protection.