Navigation performance in virtual environments varies with fractal dimension of landscape

Abstract

Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans’ ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D. In Experiment 2, participants completed a map-reading and location-judgment task in separate sets of fractal landscapes. In both experiments, task performance was highest at the low-to-mid range of D, which was previously reported as most preferred and discriminable in studies of fractal aesthetics and discrimination, respectively, supporting a theory of visual fluency. The applicability of these findings to architecture, urban planning, and the general design of constructed spaces is discussed.

The shift from life in water to life on land advantaged planning in visually-guided behavior

“…Transitioning from a poorly connected region to a highly connection region implies increased visibility and access from nearby cells. Planning at , the green fill shows the range of fractal dimensions (1.0-1.6) that are observed in typical terrestrial environments 33,34 , and the pink fill shows the range of fractal dimensions (1.9-2.0) that are observed in typical coral reefs 35,36 . (c) Environment network complexity (see Fig.…”

Relationship between Fractal Dimension and Spectral Scaling Decay Rate in Computer-Generated Fractals

“…Further consideration of the relationship between D and β is both important and timely because new studies are being performed using fractals to investigate a variety of behaviors including aesthetics [22][23][24][25][26][27], navigation [28], object pareidolia (perceiving coherent forms in noise) [29,30], sensitivity [24], and associated neural mechanisms [31][32][33]. This is especially important in aesthetics research, where there have been claims of universality in preference for patterns of moderately low complexity [23,26,[34][35][36][37].…”

“…This is especially important in aesthetics research, where there have been claims of universality in preference for patterns of moderately low complexity [23,26,[34][35][36][37]. To test this hypothesis, it is necessary to be able to translate the units of measurement of researchers who alternately use D [22,25,26,28,29,31,[33][34][35][36][37][38][39][40], β [14,24,30,32,[41][42][43][44][45][46], or, infrequently, both [23,27]. The crux of the problem, perhaps, is that D is a general parameter that quantifies complexity in a variety of patterns, whereas β is limited (at least in practice) in its ability to quantify some patterns' complexity.…”

“…The recent work of Juliani et al [28] asks individuals to navigate fractal environments. Under conditions such as these, the map typically has complexity in the range 1 < D (Coastal Edge) < 2, whereas the navigated environment has complexity in the range 2 < D (Surface) < 3, and the visually perceived scene has a spectral decay that likely falls off at a rate in the range 2 < β (Surface) < 4.…”

Geometría fractal aplicada para comparar los espacios ocupados por eritrocitos normales y esferocitos

“…Los diferentes fractales provienen de dos grandes grupos, los fractales deterministas que pueden ser algebraicos o geométricos, como por ejemplo la trayectoria de un péndulo; los indeterministas (o estocásticos) como los objetos de la naturaleza denominados salvajes [2]. La generación de estos últimos fractales implica la introducción de parámetros aleatorios, los cuales buscan una semejanza con los objetos de la naturaleza, que se caracterizan por modificaciones e irregularidades en su estructura [3,4]. Para cada tipo de fractal, existe un método matemático que permite calcular el grado de irregularidad, denominado dimensión fractal.…”