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We establish a statistical two-body fractal (STF) model to study the spectrum of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula> serves as a reliable probe in heavy-ion collisions. The distribution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula> in hadron gas is influenced by flow, quantum and strong interaction effects. Previous models have predominantly focused on one or two of these effects while neglecting the others, resulting in the inclusion of unconsidered effects in the fitted parameters. Here, we study the issue from a new point of view by analyzing the fact that all three effects induce a self-similarity structure, involving a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> two-meson state and a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> two-quark state, respectively. We introduce modification factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>q</mi><mrow><mi>T</mi><mi>B</mi><mi>S</mi></mrow></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>q</mi><mn>2</mn></msub></semantics></math></inline-formula> into the probability and entropy of charmonium. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>q</mi><mrow><mi>T</mi><mi>B</mi><mi>S</mi></mrow></msub></semantics></math></inline-formula> denotes the modification of self-similarity on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>q</mi><mn>2</mn></msub></semantics></math></inline-formula> denotes that of self-similarity and strong interaction between <i>c</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>c</mi><mo>¯</mo></mover></semantics></math></inline-formula> on quarks. By solving the probability and entropy equations, we derive the values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>q</mi><mrow><mi>T</mi><mi>B</mi><mi>S</mi></mrow></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>q</mi><mn>2</mn></msub></semantics></math></inline-formula> at various collision energies and centralities. Substituting the value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>q</mi><mrow><mi>T</mi><mi>B</mi><mi>S</mi></mrow></msub></semantics></math></inline-formula> into distribution function, we successfully obtain the transverse momentum spectrum of low-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>p</mi><mi>T</mi></msub></semantics></math></inline-formula> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>, which demonstrates good agreement with experimental data. The STF model can be employed to investigate other mesons and resonance states.