Psychophysics and Personality Factors, A Brief Report


Olga V. Mitina

Moscow State University, Department of Psychology




Frederick David Abraham

Bluberry Brain Institute, VT, USA & Psychology, Silliman University, Philippines


1. Introduction


The present paper deals with perception of time (subjective assessment of temporal intervals), complexity and aesthetic attractiveness of visual objects. Fractal pictures were chosen as stimulus material. This choice was determined by the fact that fractals can be described with the help of mathematically rigorous information measures (fractal dimension, the Lyapunov exponent, etc.). These information parameters vary in a rather broad and continuous range of real numbers, so the experimenter can easily manipulate them. Besides, fractals appear on computer monitor not as static images, but dynamically in the experimentally preset time range, and that allows assessing the subjective perception of time during which the image is being displayed. Finally, fractals are non-standard, abstract visual objects, which permit elimination of the effect of recognition and related side-effects (hidden associations, variable or confounded conditions that are difficult or impossible to control in the course of an experiment, etc.).


Fractals enable visual representation of the mathematical idea of determined chaos [Schroeder 2001; Bozhokin & Parshin, 2001]. This word combination itself contains a semantic opposition and, therefore, a certain ambiguity. A fractal curve can remain irregular and chaotic even in an indefinitely small area. In contrast to the objects of traditional Euclidean geometry like point, line, circumference, sphere, etc., which are complete forms, it is impossible to finish the drawing of a fractal. One can determine the fractal algebraically, for instance, but any finite realization is necessarily incomplete, emphasizing that a fractal is a dynamical process, more than a static one that we may view at any point in its evolution.


The semantic opposition of dynamic and static, may raise fractals from mere geometrical objects to the level of Art, in that any perceptual process is also dynamical, which may relate to the dynamics of the creation of the stimulus process being viewed, which is not surprising as biological evolution interacts with both the external and internal aspects of perception [Yevin, 2001]. It is not by chance that fractals appeared in the pictures of Dutch painter Maurice Escher even before those of mathematician Benoit Mandelbrot who gave fractals their rigorous mathematical description, which showed the static product of the fractal process as a structure consisting of parts that in a certain sense are similar to the whole [Mandelbrot, 1977 ; Peitgen & Richter, 1986]. Hence the main principle of fractal is self-affinity. 


The incompleteness of any iterative fractal process implies that imagination is necessary to complete the fractal object in human the human perceptual process. This suggests, in a certain sense, a third semantic opposition, that between a logical/mathematical process (algorithmic) and an intuitive one. Studying subjective perception Sprott [1993] suggests the interpretation of fractal dimension as the measure of fractal’s “strangeness”, and the Lyapunov exponent as the measure of its chaoticity. Studying subjective perception Sprott [1993] suggests the interpretation of fractal dimension, its degree of complexity in space, as the measure of fractal’s “strangeness”, and the Lyapunov exponent, its degree of complexity in time, as the measure of its chaotic nature.


Art and other objects (all of which are, of course, produced by dynamical processes), like fractals, can vary in their mathematical complexity. Fractal dimension and the Lyapunov exponent are the most widespread mathematical characteristics of fractals [Sprott, 1993; Abarbanel 1996]. Thus, doing research on the perception of fractal objects may reveal insights into perceptual process generally. Bearing in mind the fact that fractal dimension is the measure of information, we can say that it is a measure of the object’s “actual” complexity, this parameter providing a convenient independent variable for perceptual experiments.


One more semantic (and dynamical) opposition represented by fractal processes is between constriction and expansion existing simultaneously in the same process. Trajectories constrict infinitely on the dimensions that correspond to negative Lyapunov exponents and infinitely diverge from each other on the dimensions that correspond to positive Lyapunov exponents [Abarbanel 1996; Ott, Sauer, & Yorke 1994]. This opposition, the struggle between convergence and divergence, is responsible for the development of chaotic trajectories in dynamical systems [Abraham, Abraham, & Shaw, 1990].


2. Introduction to Study of Perception of Time, Complexity and Aesthetic Attractiveness of Visual Objects


Since William James [1890] many prominent psychologists [Fraisse, 1967; S.L. Rubinstein ; B.G. Ananjev; and many others] were interested in the problems of psychological time. Psychological time is essentially different from objective chronological time. People have individual peculiarities of time perception, for example, as smooth or uneven, compressed or stretched out, empty or rich.


The studies of the subjective length of intervals for stimuli representation and their complexity are rather controversial. Schiffman and Bobko [1974] ascertained that the more complex is the stimulus within a given interval of time, the longer seemed the time interval to the subject.  F. Macar [1996] obtained the results that the increasing of stimuli complexity lead to the perception of time intervals as shorter.


Nevertheless, his work contains references to the results of numerous empirical studies over several years indicating that the increased complexity of stimuli leads to the perception of time interval as longer. This uncertainty agrees with the hypothesis about the existence of the U-shaped (quadratic) dependence between the complexity of stimulus and the evaluation of time. According to this hypothesis simple and very complex stimuli are perceived as more lengthy in comparison with the stimuli of moderate complexity [Lomranz, 1983].


The search for mathematical correlates of the attractiveness of art, sculpture, and architecture has very old traditions—e.g., the golden mean (the limit of the Fibonacci ratio, 1.61818…—probably the most studied number in mathematics : why should the eye like it so much ?), the formulas of Leonardo da Vinci, etc. It is possible to say that Fechner laid the foundations of experimental aesthetics studying which forms and sizes are most pleasant to the eye [Schroeder, 2001; Crozie, 2002]. The study of the interdependence between the magnitude of the objective stimulus and the evoked subjective sensation is a classic field of psychophysical research. The relations between physically or mathematically measured intensiveness of auditory, visual, temporal and other signals and loudness, brightness, length perceived by man were studied since the middle of the 19th century by E. Weber, G. Fechner, S.S. Stevens [1975] and many others. For instance, the well-known Weber–Fechner Law states that within a certain range the dependence between the magnitude of physical stimulus and the evoked subjective sensation measured in some conditional units obeys the logarithmic law [Torgerson, 1958]. Early studies were mainly on acoustic, visual, haptic, and tactile stimuli. The study of more complex aspects of time perception appeared much later, including multidimensional interactions [Gregson, 1994; Stevens, 1975]. As for the study of the perception of complexity and aesthetical attractiveness of objects, these endeavors, despite their multiplicity, still remain topical. Even the meaning of the “golden section” is no clearer at present than in the times of Fechner [Crozie, 2002].


According to I. Yevin [2001] there is the optimum of arousal potential when the pleasure from aesthetical object reaches its maximum. It is quite obvious that the possibility to achieve the optimal value ФС is connected with many factors—individually  and situationally. The consideration of individual and situational factors has led to the exploration of individuality factors in such studies, such as age, gender, and personality (e.g, Eisler & Eisler, 1994, for time scaling). Thus our studies of the psychophysics of time, complexity, and aesthetics here include several measures of personality factors in order to identify if any are key to the utilization of fractal properties perceptually.


3. Methods


3.1. Apparatus and Stimuli


As stimulus material we used a program for generating strange attractors by J. Sprott [1993]. He adapted the basic program to one for presenting the stimuli and recording results from participants via a computer, in a flexible format for us. The basic algorithms for the generation of these attractors is as follows:


The iteration procedure of are difference equations of the general form:


Xn+1= a1+a2Xn+a3Xn2+a4XnYn+a5XnZn+a6Yn+a7Yn2+a8YnZn+ a9Zn+a10Zn2

Yn+1= a11+a12Xn+a13Xn2+a14XnYn+a15XnZn+a16Yn+a17Yn2+a18YnZn+ a19Zn+a20Zn2

Zn+1= a21+a22Xn+a23Xn2+a24XnYn+a25XnZn+a26Yn+a27Yn2+a28YnZn+ a29Zn+a30Zn2


We fixed the quotients ai within the interval from -4.5 to 5 and initial values X0 Y0 Z0. If after a large number of iterations (from 500000 to 10 million) the function values remain bounded in a small domain of three-dimensional state space and the largest positive Lyapunov exponent exceeds 0.005, the obtained graphic trajectory can be regarded as a usable fractal. Two dimensions are represented in the plane, and the third with a color-palette.


The Lyapunov exponent was calculated in the usual manor. For two arbitrarily close initial conditions (X0 Y0 Z0) and (X/0 Y/0 Z/0) the distances dn between the images of those points obtained at the nth step and the distances dn+1 between the images of the same points at the (n+1)th step (generated by Sprott’s program as the trajectories evolve). Then the Lyapunov exponent L equals


       L = Sn=1N  log2 (dn+1/dn)/N


After the end of iteration process we obtained the fractal dimension (also generated by the program as the trajectory evolves; the trajectory evolves too rapidly to follow visually; it appears complete early during it’s the course of its presentation; and is not a continuous trajectory, but a series of points, such that the trajectory is lost to view in the cloud of points as the stimulus becomes an image). To do so we calculated N2, the number of points in the course of the whole iteration process that lay at the distance of 0.2 from each other, and N1, the number of points that lay at the distance of 0.1 from each other. The fractal dimension F was then computed as


F =  log2(N2/N1)


For the present study we used 20 three-dimensional fractals {0.52 < F < 2.36, 0.01 < L < 0.22, r(F,L) = 0.91} that were displayed on the monitor of the computer in random order. Presentation times varied from 2 to 30 seconds. The participants had to assess the subjective complexity and aesthetic attractiveness of each fractal on the nine-point scale (from 1 to 9) and to estimate the duration of the presentation of each stimulus. The stimulus disappeared from view before the set of three questions for each was presented.


When fractals with high fractal dimension were displayed there always was a certain moment when there appeared so many points on the screen that the respondent could no longer notice the appearance of new points and it seemed that the object had already completed its shape. Therefore answering the question about the time of fractal formation the respondents tended to underestimate the time, though the tendency was not very marked.


3.2. Participants and procedure


The participants were 140 students and post-graduates of the Department of Psychology of Moscow State University. We carried out two experiments. These differed only in the durations of the presentation of the stimuli. In the first (93 Ss), the stimuli varied randomly in duration from 2 to 30 sec. In the second (47 Ss), three fixed intervals were used of 5, 15, and 25 seconds. Besides assessing the fractals,participantsanswered the questions of the follow personality inventories:


Internality inventory for determining Locus of control (Internal control orientation « external control orientation) (Rotter 1982), Eysenck Personality Questionnaire Revised (Eysenck, 1990) for determining temperamental features, 16PF Sixteen Personality Factor Questionnaire (Cattell, 1946; Cattell et al, 2002) and Spielberger's Test Anxiety Inventory (Spielberger et al., 1983, 1995) (See Table 1A-D). The participants that took part in the second series were divided into three subgroups of 15 or 16 people. This was a between-subjects design where each subgroup received just one of the three presentation times (5, 15 and 25 sec.) for all 20 fractals.


4. Results and discussion


We would note that subjective complexity and aesthetic attractiveness rather highly correlate (Table 2). For both experiments, we constructed the cluster-trees of fractals’ similarity on their aesthetic attractiveness and complexity. As one might expect both trees were very similar in their structure. Conventionally we can describe the fractals of low, middle, and high dimensionality as the following types: (1) “points and thin lines” (F < 1), (2) “lace” (1 < F < 2) and (3) “cushions” (F >  2). Figure 1 illustrates typical fractals of each type.


As the result of correlation and determination analysis (Chesnokov, 1982) we specified significant determinations of predispositions to assess presented fractals as more complex or simple, aesthetically attractive or unattractive by certain personality traits. The most robust personality determinations are follows (see Tables 1A,B,C for identification of personality factors):


Ss disposed to self-accusation, vulnerable, and diffident (O+) overtly tended to assess fractals of type 1 (separate points and lines) as very beautiful and complex. One of the possible interpretations of this fact is that those people, being uncertain, were afraid that they had missed something on the screen, failed to grasp the essence and were not competent enough to discover the complexity and beauty of that singular points and lines. After the experiment one of the respondents supposed that the program simply “made an error” on those pictures and didn’t draw the whole fractal to the end. Evidently we observe the feeling of guilt – the program worked poorly on her computer. Nevertheless, she evaluated these fractals from the first group as complex, i.e. “invented” their complexity and aesthetic attractiveness.


A tendency to regard the fractals of type 1 as complex was revealed in the participants for whom approval and support from the others was in many respects the decisive factor (Q2–). It may be connected with the desire to demonstrate a non-standard understanding of the process from the mathematical standpoint and deserve an approval from the experimenter. After all, their assessments of aesthetical attractiveness didn’t deviate from the norm. In contrast, independent people (E+), who are independent in making decisions and actions, evaluate the fractals of type 1 as the least complex. Such evaluation is based exclusively on their own perception and the opinions of others are ignored.


As we noted before, the whole sample revealed the trend to evaluate fractals with higher fractal dimension as more aesthetically attractive and complex. However, respondents with prevailing modesty, tactfulness and pliability (E–) were among those who displayed this trend most of all. It is their E+ counterparts — self-assured, independent participants, inclined rather to leadership than subordination or submission, uncompromising and disregarding authority and existing norms — that markedly differed from the whole sample and didn’t admit the aesthetic attractiveness of these fractals. One may make many hypotheses about this tendency, but more definitive answers will require more research.


Another fact, still remaining unclear, is connected with the disposition of temperamentally and emotionally stable people (NE–) to underestimate the complexity of fractals of type 2.


It is interesting to mention that although the ratings of aesthetic attractiveness of fractals of type 3 with the highest fractal dimension, given by respondents with high self-organization and self-discipline (Q3+) do not differ from average in the sample, their assessment of fractals’ complexity tends to be higher. It may be possible, that here they latently showed their ability to answer directly the question that was asked (fractals of this group actually have the highest objective complexity) and leave the emotional component “behind the brackets”. (The question of aesthetic attractiveness unequivocally touches upon the emotional sphere).


The participants with moderate emotional openness and need for communication (A±) assessed fractals of type 1 (points and lines) as most simple and mostly disliked them. These participants generally gave lower average ratings to all pictures on both attractiveness and complexity.


We revealed no personality determinant in the assessment of time intervals.


To discover the influence of the duration of presentation and fractal dimension of the stimuli on the assessment of their subjective complexity and aesthetic attractiveness we used two-factor analysis of variance. It enabled us to make the following conclusions: the time of fractal generation on the screen does not affect the assessment of its aesthetic attractiveness and complexity. Fractal dimension is the main correlate of subjective evaluation of fractal’s attractiveness and complexity (p<0.0001). The more is the fractal dimension the more attractive and complex is the fractal perceived. (Table 3).


J. C. Sprott was the first to conduct experiments on assessing fractals’ aesthetic attractiveness of. Although the number of pictures being assessed was very impressive — 7500 fractals, the number of respondents was small (7 people). Most attractive appeared fractals with fractal dimension from 1.1 to 1.5 and the Lyapunov exponent from 0 to 0.3 [Sprott 1993; Aks & Sprott 1996]. Osorio et. al [2000] used four levels of fractal dimension (and the same stimuli as used in this study) obtained a non-monotonic function of aesthetic and complexity judgments peaking in the similar fractal range as that of Sprott, namely, 1.4-1.6. The Osorio study also failed to show any simple relationship between time estimation and fractal dimension.


Mandelbrot [1977] classic establishment of fractals as mathematical discipline showed that many natural objects could have dimension. He and others have noted the beauty in fractals, perhaps because of their imitation of nature [Peitgen & Richter, 1986]. In Sprott’s opinion, the preference for fractals with relatively small Lyapunov exponent is connected with the fact that excessive chaotization of the object does not favor its harmonic perception. We obtained different results. And here we have the possibility of culture factor influence. Russians like more “dense” things. And our sample may be more representative. The Osorio study looked at age and cultural factors, but found no such clear results. We have hopes of evaluating such cultural influences in future studies.


In conclusion we would note that our hypothesis on the applicability and fulfillment of Weber-Fechner law for the perception of time, complexity and subjective attractiveness was confirmed. Namely, the subjective estimate of time, τ, obeys the logarithmic dependence from the actual time of fractal’s formation (presentation) on the screen, t:


t = 7.15LN(t) – 6.53 (R2 = 0.47).


The subjective assessment of fractal’s complexity S and aesthetic attractiveness σ obeys the logarithmic dependence upon fractal dimension F:


S = 2.56Ln(F) + 4.88 (R2 = 0.61)


s = 2.06Ln(F) +4.89 (R2 = 0.59)


and upon the Lyapunov exponent L:


S = 1.02Ln(L) + 8.07 (R2 = 0.34)


s = 0.85Ln(L) +7.53 (R2 = 0.35)


In all three cases the significance level p<0.0001.



5. Acknowledgments


This work was supported by a grant from the Russian Foundation for Basic Research. The authors wish to thank S.Fomichev for assistance in data collecting, I.Timofeev for translation this text in English, M.Gambarian for help in preparation the manuscript for publication. Clint (J.C.) Sprott kindly spent considerable time patiently adapting his strange-attractor engine for use in our series of psychophysics experiments. Deborah Aks gave us important advice on the conduct of psychophysics experiments.


6. References


Abarbanel, H., 1996. Analysis of Observed Chaotic data. NY: Springer-Verlag.


Abraham, F.D., Abraham, R.H., & Shaw, C.D., 1990. A Visual Introduction to Dynamical Systems Theory for Psychology. Santa Cruz : Aerial Press.


Aks, D.J., & Sprott, J.C., 1996. Quantifying Aesthetic preference for Chaotic pattern. Empirical Studies of the Arts, 14(1), 1-16.


Bozhokin, S.V., & Parshin, D.A., 2001, Fractals and Multifractals, [Fraktaly i Multifractaly], Izhevsk: NIC “Regular and chaotic dynamics”, (in Russian).


Cattell, R., Cattell, K., & Cattell, H., 2002. Sixteen Personality Factor Questionnaire (16PF) Institute for Personality and Ability Testing. Champaign, IL


Cattell, R.B., 1946. The Description and Measurement of Personality. New York: Harcourt, Brace and World.


Chesnokov S.V., 1982. Determinatsionnii analiz sotsialno-ekonomicheskikh dannykh (Determinational analysis of social and economic data). М.


Crozie, U.R., 2002. Gustav Theodor Fechner. Who is who - <>, (in Russian).


Eisler, A.D., & Eisler, H., (1992). Subjective Time Scaling : Influence of Age, Gender, and Type A and Type B Behavior. Chronobiologia, 21, 185-200.


Eisler, A.D., Eisler, H., & Montgomery, H., (1996). Prospective and Retrospective Time Perception : Cognitive and Biological Approaches. In, S.C. Masin (Ed.), Fechner Day, Proceedings of the Twelfth Annual Meeting of the International Society for Psychophysics, University of Padova.


Eysenck, H.J., 1990. Biological dimensions of personality. In L. A. Pervin (Ed.), Handbook of personality: Theory and research (pp. 244-276). New York: Guilford.


Fraisse, P., 1967. Psychologie du temps (2nd Ed.). Paris: Presses Universitaires de France.


Gregson, R.A.M., 1996. N-Dimensional Nonlinear Psychophysics: Intersensory interaction as a network at the edge of chaos. In E. MacCormac & M.I. Stamenov (Eds.), Fractals of Brain, Fractals of Mind (pp. 155-178). Amsterdam/Philadelphia: John Benjamins.


James, W., 1890/1952. Principles of Psychology. New York: Holt. Chicago: Britannica. (also Dover, 1951.)


Lomranz, J., 1983. Time estimation as a function of stimulus complexity and personality. Social Behavior & Personality, 11( 2), 77-82.


Macar, F., 1996. Temporal judgments on intervals containing stimuli of varying quantity, complexity, and periodicity. Acta Psychologica, 92(3 , pp. 297-308.


Mandelbrot, B.B., 1977. The Fractal Geometry of Nature. New York: Freeman.


Osorio, M., Dequito, E., Pinili, J.M., & Abraham, F.D., (2000). Judgments of Aesthetics, Time, and Complexity as a Function of the Fractal Dimension of Strange Attractors. Paper presented at the Annual Conference of the Society for Chaos Theory in Psychology and the Life Sciences, Berkeley, CA, USA.


Ott, E., Sauer, T., & Yorke, J., (eds.), 1994. Coping with Chaos. Analysis of Chaotic Data and the Exploitation of Chaotic Systems. New York: John Wiley & Sons.


Peitgen, H.-O., Richter, P.H., 1984. The Beauty of Fractals. Images of Complex Dynamical Systems. N.Y. : Springer-Verlag.


Rotter, J.B., 1982. The Development and Applications of Social Learning Theory. New York: Praeger.


Schiffman, H.R., Bobko, D.J., 1974. Effects of stimulus complexity on the perception of brief temporal intervals. Journal of Experimental Psychology, 103(1), 156-159.


Schroeder, M., (1991). Fractals, Chaos, Power Laws. Minutes from an Infinite paradise. New York: W.H.Freeman and Company.


Spielberger, C.D., Ritterband, L.M., Sydeman, S.J., Reheiser, E.C.,& Unger, K.K., 1995. Assessment of emotional states and personality traits: Measuring psychological vital signs. In J.N.Butcher (Ed.), Clinical Personality Assessment (pp. 42-58). New York: Oxford University Press.


Spielberger, C.D., Gorsuch, R.L., Lushene, R., Vagg, P.R., & Jacobs, G.A., 1983. Manual for the State-Trait Anxiety Inventory (Form Y) ("self-evaluation questionnaire"). Palo Alto, CA: Consulting Psychologists Press. 


Sprott, J.C., 1993. Strange Attractors: Creating Patterns in Chaos. New York: M&T Books.


Stevens, S.S., 1975. Psychophysics : Introduction to its Perceptual, Neural, and Social Prospects. New York: Wiley.


Torgerson, W.S., 1958. Theory of Methods of Scaling. New York: John Wiley & Sons.


Yevin, I., 2001. Synergetic of Brain and Synergetic of Art, [Sinergetika Mozga i Sinergetika Iskusstva]. Moscow: Geos, (in Russian).



Tables below ¯

Table 1A. 16PF Sixteen Personality Factor Questionnaire



Factor Name

Low index of factor

High index of factor



Psychomedical term



Psychomedical term




Reserved, impersonal, detatched, formal, aloof



Outgoing, kindly, easygoing, participating, likes people






Less intelligent

Lower scholastic mental capacity



More intelligent, bright

Higher scholastic mental capacity


Emotional Stability

Affected by feelings

Emotionally less stable, easily annoyed, upset

Lower ego strength

Emotionally stable

Mature, faces reality, calm

Higher ego strength




Humble, mild, easily led, accommodating, not assertive



Assertive, aggressive, stubborn, competitive, bossy






Restrained, prudent taciturn, serious



Spontaneous, heedless, expressive, cheerful





Disregards rules, self­indulgent

Weaker superego strength



Conforming, moralistic, staid, rule­bound

Stronger superego strength




Threat sensitive, timid, hesitant, intimidated



 Venturesome, uninhibited, can take stress





Self-reliant, no-nonsense, rough, realistic



 Sensitive, overprotected, intuitive, refined






Accepting conditions, easy to get on with



Hard to fool, distrustful, skeptical





Concerned with 'down to earth' issues, steady



Absent­minded, absorbed in thought, impractical





Unpretentious, open, genuine, artless



Polished, socially aware, diplomatic, calculating





Secure, feels free of guilt, untroubled, self­satisfied

Untroubled adequacy



Self­blaming, guilt­prone, insecure, worrying

Guilt proneness




Respecting traditional ideas

Conservatism of temperament



Liberal, critical, open to change






A 'joiner' and sound follower, listens to others

Group adherence



Resourceful, prefers own decisions






Disciplined, self­conflict

Lax, careless of social rules

Low integration

Following self­image

Socially precise, compulsive

High self­concept control




Tranquil, composed, has low drive, unfrustrated

Low ergic tension


Frustrated, overwrought, has high drive

High ergic tension


Table 1B. Internality inventory



Low index of scale


High index of scale


External control orientation


Internal control orientation


A belief about that the outcomes of our actions are contingent on the events outside our personal control, are under the control of powerful others or is determined by fate, luck or chance


A belief about that the outcomes of our actions are contingent on what we do, are directly the result of behavior




General External control orientation

External control orientation in successes

External control orientation in failures




General Internal control orientation

Internal control orientation in successes

Internal control orientation in failures


Table 1C. Eysenck Personality Questionnaire (EPQ).



Factor Name

Low index of factor

High index of factor








In need of peace and quiet


Outgoing, talkative, high on positive affect (feeling good), and in need of external stimulation




High activation thresholds and good emotional control, experience negative affect only in the face of very major stressors, calm and collected under pressure


Unable to inhibit or control their emotional reactions, experience negative affect (fight-or-flight) in the face of very minor stressors.

easily nervous or upset






Aggressive, Assertive, Egocentric, Unsympathetic, Manipulative, Achievement-oriented, Dogmatic, Masculine, Tough-minded


Table 1D. Spielberger's Test Anxiety Inventory



Factor Name



State anxiety

refers to transient emotional states, consisting of "consciously perceived feelings of tension, apprehension, nervousness, and worry, and associated with activation or arousal of the autonomic nervous system, [which] vary in intensity and fluctuate over time as a function of perceived physical or psychological danger" "(Spielberger et al., 1995, p. 44).


Trait anxiety

"is conceptualized in terms of relatively stable individual differences in anxiety proneness "(Spielberger et al., 1995, p. 44).


Table 2. Significant correlations between mathematical and psychological characteristics


Lyapunov exponent

Aesthetic attractiveness

Subjective complexity

Fractal Dimension

.907 (.000)

.664 (.002)

.718 (.001)

Lyapunov exponent


.594 (.006)

.626 (.003)


Aesthetic attractiveness



.934 (.000)


The parentheses contain the level of significance.


Table 3. Results of ANOVA

Aesthetic attractivenes




Fractal Dimension







2-Way Interaction

Fractal Dimension + Time



Subjective complexity




Fractal Dimension







2-Way Interaction

Fractal Dimension + Time



Three Levels of Fractal Dimensions:     Three Levels of Time:

<1                                                       5 sec

from 1 to 2                                          15 sec

>2                                                       25 sec