Fractal aspects of natural growth

doi:10.1016/0040-1625(94)90040-X

Technological Forecasting and Social Change

Volume 47, Issue 1, September 1994, Pages 63-73

https://doi.org/10.1016/0040-1625(94)90040-X Get rights and content

Abstract

The work presented here puts forward a fractal aspect of natural growth. The S-shaped pattern of a logistic function is analyzed in terms of several constituent logistic functions. The approach sheds light on two familiar phenomena: the undulatory evolution of growth, which gives rise to an alternation between high-and low-growth periods, and the increasingly noticeable shrinking life cycle of products. There are some economic and political implications for the European nations. A quantitative example is given for computer sales from Digital Equipment Corporation. The approach is further generalized to suggest that any growth process can be analyzed in terms of natural-growth subprocesses. Applied to human growth this analysis yields precise definitions for the timing of transitions such as babyhood to childhood, and childhood to adolescence.

References (12)

T. Modis et al.
Chaoslike States Can Be Expected Before and After Logistic Growth
Technological Forecasting & Social Change
(1992)
C. Marchetti
Society as a Learning System: Discovery, Invention and Innovation and Innovation Cycles Revisited
Technological Forecasting & Social Change
(1980)
C. Marchetti
The Automobile in a System Context: The Past 80 Years and the Next 20 Years
Technological Forecasting and Social Change
(1983)
C. Marchetti
Fifty-Year Pulsation in Human Affairs, Analysis of Some Physical Indicators
Futures
(1986)
H.O. Peitgen et al.
The Beauty of Fractals
(1986)
J. Gleick
Chaos
(1987)

There are more references available in the full text version of this article.

Cited by (37)

Forecasting: theory and practice
2022, International Journal of Forecasting
Citation Excerpt :
S-curves enter as modular components in many intricate natural patterns. One may find S curves inside S curves because logistics portray a fractal aspect; a large S curve can be decomposed in a cascade of smaller ones (Modis, 1994). One may also find chaos by rendering the logistic equation discrete (Modis & Debecker, 1992).
Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts.
We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.
Methodological support for prospective studies in New Concept Development
2015, Procedia Engineering
Industrial leaders, in order to stay competitive, take decisions on the basis of estimations of what the future socio-economic environment will look like. Several approaches exist for the conduction of studies sought to make this estimation reliable. We distinguish the classical prospective approach, based on works of French philosopher Gaston Berger and approaches combining the works of G. Altshuller with the theory of logistic growth curves. In order to combine the advantages of the two strategies, we suggest the combination of several tools and methods for the “Opportunity Identification phase” of the cited New Concept Development Model. We then conclude the article with an applicative case study.
Sustainability of catch-up growth in the extended European Union
2014, Journal of Cleaner Production
Citation Excerpt :
Accelerating growth is characteristic of the first stage, while roughly linear growth exists in the second phase, and decelerating growth that asymptotically approaches saturation characterises the final stage. Logistic growth based on the concept of limiting resources reflects the action of natural law (Modis, 1994; Scarpello and Ritelli, 2003; Guerrini, 2011). The rate of growth (the first fluxion of logistic equation) is bell shaped with the extreme in the middle of the time limits.
This paper analyses the compatibility of growth and sustainability in the European Union (EU) including a new EU member states from the former Soviet bloc (EU₁₀). The extension of EU borders, financial and technological support stimulated rapid convergence and decreased the socio-economic differences between the old (EU₁₅) and newly accepted EU member states. The transition from a command to a market economy resulted in the remarkable increase in resource efficiency and other positive aspects of sustainability. Along with 1.5 times increased GDP, final energy consumption decreased by 20%, greenhouse gases emissions by 25% and the emissions of acidifying compounds were halved during the period from the collapse of former Soviet bloc to the recent economic crisis. However, the per capita production and consumption in EU₁₀ is still approximately half that of EU₁₅, and further catch-up growth should be expected ensuring that economic and social cohesion is not achieved at the expense of increased environmental impact.
Decelerated economic growth is a feature characteristic of mature economies and the GDP growth rate in EU₁₅ states decreased almost 2.5 times during the last 50 year. Similar trends are characteristic of other developed countries, and market economies have adapted to this trend. Even with a decelerated growth rate, the ecological footprint in developed countries currently exceeds three and more times the allowable limits and almost two-thirds of the ecological footprint relates to traditional energy. De-fossilisation by a greater increase in energy efficiency, use of renewable energy, and more intense material recovery is the most promising option for reducing the ecological footprint of these countries. Deceleration of the economic growth rate supplemented by the aforementioned options is a hard but realistic track leading to the reduction of ecological footprint in developed countries to allowable limits without radical de-growth in consumption and production that can result in unpredictable and unacceptable consequences.
Application of S-shaped curves
2011, Procedia Engineering
This paper deals with the application of S-shaped curves in the contexts of inventive problem solving, innovation and technology forecasts. After explaining the origin of the logistic S-curve its application, as seen in publications from different domains, is reviewed. Despite much criticism and the failure to apply the logistic function for long-term forecasting, it continues to be a popular model for describing the evolution of systems (technological, economical, social and others) over time. This paper can help researchers and practitioners to understand the scope of application of S-shaped patterns, their limitations, and peculiarities.
Logistic substitution model and technological forecasting
2011, Procedia Engineering
In this paper the application of several models, based on the logistic growth function (simple logistic, component logistic and logistic substitution models) in the context of technology change forecasting is discussed. The main idea of this paper is to revise existing models and arrange working hypotheses for future research. First, the features of a simple logistic model are presented, different types of competition are discussed and a component logistic model is briefly presented. Second, logistic substitution models in the context of long-term technological forecasting are reviewed. Third, some hypotheses about how to improve the reliability of the logistic substitution model for studying the technological future are proposed.
On Niall Ferguson's "Complexity and Collapse"
2010, Technological Forecasting and Social Change

View all citing articles on Scopus

^∗: Theodore Modis is a physicist and a strategy consultant at Digital Equipment Corporation International.

View full text

Fractal aspects of natural growth

Abstract

Technological Forecasting & Social Change

Technological Forecasting & Social Change

Technological Forecasting and Social Change

Futures

The Beauty of Fractals

Chaos