particularly the Hausdorff Dimension (HD) which can serve both as a mathematical tool and a socially

responsive framework for improving equity in skin cancer detection. Using a dataset of 155 dermoscopic images,

HD-based features were integrated with a MATLAB neural-network classifier, achieving a baseline diagnostic

accuracy of 78%. The model was then conceptually expanded using simulated crosscultural datasets to evaluate

fairness, accessibility, and inclusiveness. 87.4% was achieved on the expanded, simulated dataset. Accuracy of

87.4% indicate that HD descriptors are able to capture the geometric irregularities of malignant lesions more

objectively than conventional visual methods, offering a pathway toward earlier, non -invasive, and cost-

efficient screening. From a social - science perspective, the convergence of artificial intelligence (AI) and fractal

geometry highlights the ethical need to democratise healthcare technologies. Ultimately, this study positions

“fractal intelligence” as a form of social innovation and translating computational precision into more equitable

majority occurring in high-income regions where early screening is widely available [1]. In contrast, individuals

structural barriers, such as distance from specialist care, high diagnostic costs, and delayed laboratory

confirmation, which often result in late detection and higher mortality rates [2]. These disparities illustrate how

Traditional diagnostic approaches rely heavily on dermatologists’ visual assessments and invasive biopsies, both

of which depend on specialised expertise and laboratory infrastructure [3]. While effective, these methods place

logistical and psychological burdens on patients and reinforce a centre-periphery divide in healthcare access.

From a social-science perspective, the continued reliance on manual diagnosis reflects how structural and

Within this context, fractal analysis offers a distinctive contribution. Based on Mandelbrot’s concept of self-

similarity, fractal geometry provides a mathematical means to measure the space-filling complexity of irregular

natural forms, including skin -lesion boundaries [7]. Among its variants, the Hausdorff Dimension (HD) has

shown strong potential for distinguishing malignant from benign lesions by quantifying how structural detail

increases with magnification [8]. Previous studies demonstrate that malignant lesions typically exhibit higher

This study extends the mathematical concept of HD into the realm of social innovation. Rather than viewing

fractal analysis solely as an algorithmic enhancement, it reframes HD computation as a tool for democratising

diagnostic access. By translating qualitative clinical observations into quantitative descriptors, HD-based

analysis can support community clinics, mobile–health initiatives, and teledermatology platforms in providing

[6]. Third, many AI systems lack transparency, making it difficult for communities and clinicians to fully trust

Fractal geometry offers a potential remedy by providing a scale-invariant, observer-independent method of

quantifying lesion irregularity. However, its adoption has been slow, largely because previous implementations

have focused on computational performance rather than social adaptability. This study therefore positions fractal

intelligence, the integration of fractal mathematics with socially oriented AI, as a paradigm that can bridge

The main aim of this study is to assess how fractalbased analysis, using the Hausdorff Dimension (HD) and

supported by AI classification, can improve diagnostic accuracy while promoting inclusivity in healthcare

The significance of this study extends beyond the computational accuracy of HD-based analysis. From a

technical standpoint, fractal geometry introduces a scale-invariant and quantifiable metric that enhances

diagnostic reproducibility while reducing observer variation. From a social perspective, it supports the diffusion

of diagnostic knowledge in ways that make high-level analytical capability more accessible to underserved

This study followed a structured, step by step analytical framework designed to extract fractal features from

skin‑lesion images and classify them using an artificial‑intelligence model. The full workflow begins with image

consistent colour representation. Each photograph was labelled by dermatologists as either benign or malignant,

forming the ground-truth reference for supervised model training. There are 80 benign images and 75 malignant

images. Type of skin disease known as melanoma, vascular-lesion, basal cell carcinoma and squamous cell

carcinoma are cancerous. While nevus, seborrheic-keratosis, solar-lentigo, actinickeratosis and dermatofibroma

Before analysis, each image went through a comprehensive preprocessing pipeline to improve clarity and ensure

reliable feature extraction. Images were resized for consistency, converted to greyscale, and filtered using

median and morphological opening techniques to minimise noise without compromising edges. Lesion

segmentation was performed using Otsu thresholding followed by Canny edge detection, producing a clean

The Hausdorff Dimension (HD) was calculated to quantify how the lesion’s spatial detail changes with scale,

malignant lesions generally exhibit more chaotic, uneven borders, HD serves as a sensitive marker of

malignancy. Boundary contours extracted during preprocessing were used as inputs to the box‑counting

A feed‑forward back‑propagation neural network (BPNN) was trained to classify images based on their

extracted fractal features. The model used the Levenberg-Marquardt optimization algorithm with an adaptive

learning rate of 0.01 and a performance goal of 10⁻⁵. There is one neuron at the input layer, ten neurons at the

hidden layer and two neurons at the output layer in the structure of neural network(BPNN). The dataset was

divided into training, validation, and testing subsets using a 70 : 15 : 15 ratio. Five ‑fold cross‑validation further

To assess diagnostic capability, accuracy, sensitivity, and specificity were calculated from the confusion matrix

(TP, TN, FP, FN). Following Responsible AI principles, fairness and interpretability metrics were also included.

These additional indicators evaluated how evenly the system performed across diverse skin‑tone groups and

Although the hybrid dataset significantly improves generalisability, simulated samples cannot fully replace

genuine, region‑specific images. Fairness metrics were based on approximated skin‑tone groups rather than

verified demographics. Additionally, while HD provides strong boundary ‑based insight, handcrafted features

may fail to capture deeper spatial cues that deep‑learning models can learn automatically. Future research may

combine fractal descriptors with transfer learning or attention ‑based architectures for richer contextual

Using the combined dataset, the model’s performance was assessed through accuracy, sensitivity, specificity,

Fractal descriptors, including HD, Lacunarity, and Fractal Entropy were compared against conventional texture

features such as GLCM statistics. Using the same neural‑network architecture, fractal‑based classification

in overall accuracy. This reinforces the observation that fractal geometry captures subtle shape irregularities

To assess interpretability, 15 dermatologists and medical trainees reviewed HD overlay visualisations. Their

decision ‑making agreed with the model’s predictions 83% of the time. Participants reported that fractal overlays

undermines, professional expertise. This trust is essential for adoption, especially in clinical environments

who mastered the overlays began mentoring others, creating informal peer-to-peer learning networks. This

horizontal spread of knowledge mirrors the fractal principle itself, small patterns replicating at broader scales

Quantitative results support this observation. Although diagnostic time decreased by an average of 32%, none

of the clinicians reported feeling that their professional autonomy was threatened. Instead, they valued the

reduced cognitive burden during complex visual assessments. This shift, from intensive labour to expert

Fractal explainability reduces some of this burden by making machine logic visible, yet continued ethical

Traditional dermoscopic workstations can cost over USD 15,000, placing them beyond reach for many clinics.

The fractal-AI system, by contrast, operates on standard computers using open-source tools, lowering costs by

more than 90%. This affordability aligns with the principles of inclusive innovation, which treat cost reduction

Moreover, the system supports edge-computing deployment. Clinics with limited internet access can still run

available. This resilience reflects the appropriatetechnology approach advocated in development economics,

principles, it anticipates inequality, invites participatory evaluation, adjusts through feedback, and maintains