Multifractal Analysis of the Distribution of Three Grammatical Constructions in English Texts

Figures & data

Table 1. Descriptions of texts selected for MFA in this study.

No	Category	Text name	Sourced from	Section excerpted	Word count
1	Literary texts (Sourced from published novels)	Literary text 1	The Maze Runner (2009, by James Dashner)	Chapter 2	1139
2		Literary text 2	The Fault in Our Stars (2012, by John Green)	Chapter 2	1101
3		Literary text 3	Gone Girl (2012, by Gillian Flynn)	Chapter 1	1147
4	Children’s literary texts (Sourced from fairy tales that are used as reading materials in schools in the UK)	Children text 1	Little Red Riding Hood	All	247
5		Children text 2	Three Little Pigs	All	619
6		Children text 3	Hansel & Gretel	All	569
7	Academic texts (Sourced from published journal articles)	Academic Text 1	Text-linguistic approaches to register variation (2019, by Douglas Biber, Register Studies)	Section 4 Discussion (1 paragraph) + Section 5 Discussion/Conclusion (whole section)	1195
8		Academic Text 2	Technical disruption in foreign language teaching: The rise of simultaneous machine translation (2018, by Scott Crossley, Language Teaching)	Counter argument section (1 paragraph) + Implication and conclusion (whole section)	1116
9		Academic Text 3	Investigating variability in L2 development: Extending a complexity theory perspective on L2 writing studies and authorial voice (2020, by Gary Fogal, Applied Linguistics)	Discussion (whole section) + Conclusion (paragraph 1).	1128

Figure 1. FVP constructs in the Little Red Riding Hood.

Table 2. An example of tally sheet for FVP constructions in the Little Red Riding Hood.

Level of iteration	Measurement box size	Box number	Tally	Probability $P_i\left(\mathit{\epsilon }\right)$
k = 1	ε =1	1	40	1
k = 2	ε = 1/2	1	20	0.5
		2	20	0.5
k = 3	ε = 1/4	1	9	0.225
		2	11	0.275
		3	9	0.225
		4	11	0.275
k = 4	ε = 1/8	1	3	0.075
		2	6	0.15
		3	7	0.075
		4	4	0.1
		5	5	0.125
		6	4	0.1
		7	7	0.175
		8	4	0.1
Repeat the process until k = 9; ε = 1/256

Table 3. Satisfying the criteria of multifractality.

Criterion	Finite verb phrases
D0 > D1 > D2		D0	D1	D2
		0.764	0.738	0.713
	R^2	0.962	0.964	0.964
An inverse S-shape for the Dq-q spectrum
A non-linear plot of τq with respect to q (as evident in the bent after point 0)
A unimodal curve for the f(α)-α spectrum

Table 4. The generalised correlation Dimensions of FVP, NP, and HN in all 9 texts.

		Generalised Correlation Dimension
No	Text		FVP					NP					HN
			q = −20	q = 0	q = 1	q = 2	q = 20	q = −20	q = 0	q = 1	q = 2	q = 20	q = −20	q = 0	q = 1	q = 2	q = 20
1	Literary Text 1	Dq	0.967	0.828	0.803	0.782	0.673	1.12	0.899	0.883	0.871	0.813	1.02	0.893	0.879	0.866	0.745
		R^2	0.936	0.973	0.974	0.975	0.973	0.955	0.975	0.975	0.975	0.974	0.965	0.975	0.975	0.975	0.969
2	Literary Text 2	Dq	0.971	0.845	0.826	0.809	0.7	1.12	0.902	0.887	0.877	0.822	1.03	0.891	0.877	0.865	0.773
		R^2	0.94	0.973	0.974	0.974	0.973	0.952	0.974	0.975	0.975	0.975	0.963	0.975	0.975	0.975	0.973
3	Literary Text 3	Dq	0.942	0.815	0.792	0.77	0.637	1.06	0.902	0.889	0.88	0.83	1.02	0.894	0.882	0.871	0.785
		R^2	0.942	0.973	0.974	0.974	0.967	0.966	0.974	0.975	0.975	0.974	0.968	0.975	0.975	0.975	0.971
4	Children Text 1	Dq	0.826	0.738	0.721	0.702	0.574	1.02	0.845	0.832	0.821	0.764	1.01	0.838	0.813	0.79	0.681
		R^2	0.895	0.942	0.944	0.945	0.941	0.943	0.947	0.947	0.947	0.942	0.932	0.948	0.948	0.949	0.938
5	Children Text 2	Dq	0.939	0.812	0.779	0.746	0.617	1.05	0.878	0.864	0.854	0.798	1.02	0.874	0.859	0.845	0.756
		R^2	0.934	0.963	0.964	0.964	0.946	0.957	0.964	0.964	0.964	0.96	0.957	0.964	0.965	0.965	0.962
6	Children Text 3	Dq	0.93	0.824	0.805	0.786	0.651	1.07	0.878	0.86	0.846	0.77	1	0.871	0.855	0.848	0.767
		R^2	0.928	0.963	0.964	0.965	0.957	0.958	0.964	0.965	0.965	0.964	0.95	0.965	0.962	0.965	0.966
7	Academic Text 1	Dq	0.885	0.764	0.738	0.713	0.576	1.1	0.901	0.891	0.884	0.848	0.99	0.893	0.88	0.868	0.754
		R^2	0.904	0.962	0.964	0.964	0.959	0.959	0.974	0.975	0.975	0.975	0.966	0.975	0.975	R0.975	0.971
8	Academic Text 2	Dq	0.894	0.778	0.756	0.736	0.61	1.1	0.901	0.89	0.882	0.843	0.981	0.89	0.878	0.867	0.785
		R^2	0.939	0.966	0.968	0.969	0.96	0.965	0.974	0.975	0.975	0.976	0.965	0.975	0.975	0.975	0.975
9	Academic Text 3	Dq	0.867	0.794	0.776	0.754	0.59	1.07	0.903	0.896	0.891	0.861	1.01	0.895	0.882	0.87	0.795
		R^2	0.939	0.965	0.966	0.967	0.949	0.961	0.974	0.975	0.975	0.975	0.966	0.975	0.975	0.975	0.973

Figure 2. The text split into two.

Figure 3. Global spectrums of FVP distribution in all 9 texts.

Figure 4. Global spectrums of NP distribution in all 9 texts.

Figure 5. Global spectrums of HN distribution in all 9 texts.