A fractal is a geometric figure where each part has the same statistical character as the whole. Fractals are useful in modeling complex structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.
Given that definition, One example where history could be modeled as a Fractal would be populations where the scale would be both #of people in the population and time. History is often studied at the civilization level, the collective experience, but also exists as a series of smaller experiences. Such as a battle's outcome is made up of division, platoon, company and individual soldiers experiences. We say Meade won the battle of Gettysburg in the U.S Civil War, but to study this we can also strive to understand the individual experiences which resulted in the collective experience.
- The 20th Maine on Little Round Top
- The 2th Regiment of the New York Militia on Cemetery Ridge
- The Army of Northern Virginia and high water mark of the Confederacy
That might be an example. Fractals like the Mendelbrote Set are infinitely detailed and reveal infinite granularity as one drills in from the larger scale. I guess if you think of individual groups as fractions of populations, using Geometric Series or Geometric Progression one could theoretically drill in infinitely, given an large enough population. Although ultimately one would be limited by the fact populations aren't infinite divisible unless time is part of the scale, because they are made up of distinct individuals which unlike mathematical theory are not infinitely divisible. My thought is this scale could be further increased, if it was compounded with time allowing for further expansion. Historic time is limited, although the limit goes back beyond what we can see, the future is perhaps unlimited (theoretically in a non Doctor Strange Love sense).
Doesn't fit perfectly though because fractals like the Mendelbrote Set are both infinitely expandable and infinitely contractable. Zoom both ways. But there are numerous examples of fractals being used for modeling where they are only zoomable, and not infinitely so. The pineapple, coast lines, or a lightning bolt.
I've heard taught history being more cyclical (although imperfectly so) or more specifically circular. History repeats itself, thus knowing where you've been, one can better understand where civilization might be heading. That also applies itself to fractals as fractals often at the same or even different levels on the given scale repeat patterns.
Examples of Cyclical Theories applied to History:
- Dynastic cycle - dynasty rises to a political, cultural, and economic peak and then, because of moral corruption, declines, loses the Mandate of Heaven, and falls, only to be replaced by a new dynasty. The cycle then repeats under a surface pattern of repetitive motifs.
- Kondratiev wave - history of civilizations are broken up into periodic waves. A wave ranges from forty to sixty years, the cycles consist of alternating intervals of high sectoral growth and intervals of relatively slow growth.
- Social Cycle Theory - Social cycle theories are among the earliest social theories in sociology. Unlike the theory of social evolutionism, which views the evolution of society and human history as progressing in some new, unique direction(s), sociological cycle theory argues that events and stages of society and history are generally repeating themselves in cycles.
- Tytler Cycle - "A democracy cannot exist as a permanent form of government. It can only exist until the majority discovers it can vote itself largess out of the public treasury. After that, the majority always votes for the candidate promising the most benefits with the result the democracy collapses because of the loose fiscal policy ensuing, always to be followed by a dictatorship, then a monarchy”.
Another example might be the relationship between the ascendence of pragmatic secular liberalism and messianic religious conservatism in the United States .
As detailed by former Kennedy aid and now historian Arthur M. Schlesinger Jr. in his book The Cycles of American History
Since the founding of the country the tension between these two often opposed philosophies have influenced public policy. When the national mood favors a focus on public purpose, liberals are ascendant.
- Franklin Delano Roosevelt and his Great Depression and WW2 fighting administrations
- Lyndon Baines Johnson and his war on poverty and space programs.
When citizens grow weary of activism, they trend to private interests and conservative rule.
- Ronald Reagan and his administrations general theme of favoring private sector solutions and keeping the government out of peoples business. Smaller less obtrusive government.