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FractalBrainNet: Emulating Brain Dynamics through Fractal Architectures
Slide 1: Title Slide
FractalBrainNet: A Novel Approach to Neural Network Architecture

Inspired by Brain Dynamics and Fractal Geometry

Presenter: Gemini (on behalf of Junior and Jose R. F. Junior's Theoretical Work)
Date: May 31, 2025

Slide 2: Introduction - The Vision
The Challenge:

Despite significant advances in AI and deep learning, Artificial Neural Networks (ANNs) still struggle to fully capture the intricate complexities and dynamics observed in the human brain.
Biological brains exhibit hierarchical organization, parallel processing, and adaptive capabilities across multiple scales.
Our Proposal: FractalBrainNet

A theoretical and architectural model that integrates concepts from fractal geometry with deep neural network architectures.
Goal: To develop an ANN capable of emulating the complexities and dynamics of the human brain, leveraging the self-replication and self-similarity inherent in fractals.
Slide 3: Foundational Concepts - Inspirations
Fractal Geometry & Natural Structures:

Fractals are geometric forms exhibiting self-replicating patterns at different scales (e.g., mountains, tree branches, blood vessels).
This property allows for complex structures to emerge from simple generative rules.
Application to Brain: The brain's intricate connections and hierarchical organization suggest a potential fractal-like underlying structure.
The Original FractalNet (Larsson et al., ICLR 2017):

A pioneering deep neural network architecture based on self-similarity.
It uses recursive expansion rules to build deep networks without explicit residual connections.
Demonstrated that path diversity and effective depth (rather than just residual connections) are key to ultra-deep network success.
FractalBrainNet extends this core idea, embedding fractal rules at each network depth level.
Cerebral Dynamics & Brain Processing:

The human brain processes information in a distributed and parallel manner, with neuronal networks organized hierarchically across multiple scales.
Different brain regions and frequency bands (alpha, beta, gamma, theta) contribute to distinct cognitive functions.
FractalBrainNet aims to replicate these multi-scale, hierarchical dynamics.
Slide 4: FractalBrainNet Architecture - Overview
FractalBrainNet is designed as a deep convolutional neural network with several specialized modules that integrate fractal principles and brain-inspired dynamics:

Fractal Pattern Generation: Defines the underlying fractal "connectivity" or "mask."
Cerebral Dynamics Module: Simulates multi-frequency brain-like processing.
Fractal Neural Block: The core recursive, self-similar building block.
Adaptive Scale Processor: Handles multi-scale feature integration.
Hierarchical Staging: Sequential arrangement of Fractal Neural Blocks.
Global Attention & Meta-Learning: For enhanced adaptability and cognitive emulation.
Slide 5: Key Architectural Components - I
1. Fractal Pattern Generator (FractalPatternGenerator class)

Purpose: To generate base fractal patterns (e.g., Mandelbrot, Sierpinski, Julia sets) that influence the network's internal connectivity and activation flow.
Mechanism: These patterns serve as attention masks or weighting factors within the neural modules, guiding information processing based on fractal geometry.
Mandelbrot Connectivity: Generates a connectivity matrix based on iteration counts for points within the Mandelbrot set.
Sierpinski Connectivity: Creates a sparse, self-similar pattern resembling the Sierpinski triangle.
Julia Connectivity: Similar to Mandelbrot, but based on the Julia set, allowing for diverse fractal structures.
2. Cerebral Dynamics Module (CerebralDynamicsModule class)

Inspiration: Simulates the brain's distributed and parallel processing across different "frequency bands."
Functionality:
Applies a generated fractal pattern as a spatial attention mask to input features.
Processes input through multiple parallel convolutional layers (e.g., alpha_processing, beta_processing, gamma_processing, theta_processing) representing different processing "scales" or "frequencies."
Integrates these multi-scale outputs using a fusion layer and adaptive Layer Normalization.
Includes a residual connection for stable learning.
Slide 6: Key Architectural Components - II
3. Fractal Neural Block (FractalNeuralBlock class)

Core Recursion: Implements the fractal expansion rule, similar to the original FractalNet:
Base Case (Level 1): A standard convolutional layer followed by CerebralDynamicsModule, BatchNorm, and GELU activation.
Recursive Step (Level > 1): Consists of two parallel branches:
Deep Branch: Two stacked FractalNeuralBlocks of the previous level, enabling deeper pathways.
Shallow Branch: A single convolutional layer followed by CerebralDynamicsModule, BatchNorm, and GELU, representing a shorter path.
Fractal Attention: A learnable mechanism to adaptively combine the outputs of the deep and shallow branches, acting as a dynamic weighting.
Drop-Path: A regularization technique (similar to dropout) applied to the output of each block, which helps prevent co-adaptation and encourages path independence.
4. Adaptive Scale Processor (AdaptiveScaleProcessor class)

Inspiration: Emulates the brain's ability to process information at different levels of abstraction simultaneously.
Functionality:
Processes input features using convolutional layers with different kernel sizes (local_processor (1x1), regional_processor (3x3), global_processor (5x5)).
Concatenates these multi-scale features and fuses them via a convolutional layer with BatchNorm and GELU.
Also includes a residual connection for robust feature propagation.
Slide 7: Overall Architecture & Advanced Features
FractalBrainNet (FractalBrainNet class)

Stem: Initial convolutional layers with AdaptiveScaleProcessor for early feature extraction.
Fractal Stages: A sequence of stacked FractalNeuralBlocks, with progressive channel increase and adaptive pooling between stages.
Global Attention (nn.MultiheadAttention): A multi-head self-attention mechanism applied to the global features extracted from the network, inspired by the brain's ability to integrate information across distant regions.
Continuous Learning (Meta-Learner):
An optional meta_learner module aims to facilitate continuous adaptation and generalization.
It learns to adjust the global features, providing a form of "residual meta-learning."
Neuroplasticity-Inspired Weight Initialization: Weights are initialized using methods like Kaiming Normal and Truncated Normal, with an emphasis on fan_out for convolutional layers, reflecting dynamic connectivity.
Classification Head: Standard pooling and linear layers for final output (e.g., classification).
Slide 8: Expected Outcomes & Potential Impact
Enhanced Generalization & Adaptability: By mimicking hierarchical and multi-scale brain dynamics, FractalBrainNet is expected to generalize better to complex, multi-scale datasets.
Improved Efficiency & Interpretability: The fractal approach may reduce the need for excessively complex, hand-tuned architectures, potentially leading to more efficient and interpretable networks.
Insights into Biological Neural Networks: The emergent patterns within FractalBrainNet after training could offer valuable insights into the organization and functioning of biological neural networks.
New Avenues for Advanced AI: This theoretical framework opens new perspectives for developing more brain-like Artificial Intelligence.
Slide 9: Project Status & Future Directions
Current Status:

Theoretical model proposed in Jose R. F. Junior's LinkedIn article (August 2024).
Conceptual PyTorch implementation providing a robust framework for exploration.
Demonstration of core components: fractal pattern generation, cerebral dynamics, recursive blocks, and multi-scale processing.
Future Research:

Extensive Experimental Validation: Rigorous benchmarking on large-scale datasets (e.g., ImageNet, complex time-series data).
Optimization of Fractal Parameters: Exploring the impact of different fractal patterns, levels, and resolutions.
Deeper Integration of Chaos Theory: Investigating explicit incorporation of Feigenbaum constants or other chaotic dynamics.
Advanced Meta-Learning Strategies: Developing more sophisticated continuous learning capabilities.
Neuroscientific Validation: Collaborations to validate the model's emergent properties against actual brain data.
Hardware Acceleration: Optimizing for specialized hardware (e.g., neuromorphic chips) for efficient brain-inspired computing.
Slide 10: Acknowledgements & References
Special Thanks to:

Jose R. F. Junior for the innovative theoretical proposal of FractalBrainNet.
Gustav Larsson, Michael Maire, and Gregory Shakhnarovich for their foundational work on the original FractalNet.
Key References:

Junior, J. R. F. (2024, August 19). FractalBrainNet. LinkedIn Pulse.
Larsson, G., Maire, M., & Shakhnarovich, G. (2017). FractalNet: Ultra-Deep Neural Networks without Residuals. ICLR 2017. (arXiv:1605.07648)
Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. W. H. Freeman and Co.
Sierpinski, W. (1915). On the theory of fractions. Mathematische Annalen.

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FractalBrainNet-v2.py

@@ -0,0 +1,557 @@
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+import numpy as np
+import math
+from typing import Optional, List, Tuple, Dict, Callable
+from enum import Enum
+
+class FractalPatternType(Enum):
+    """Tipos de padrões fractais suportados pela FractalBrainNet"""
+    MANDELBROT = "mandelbrot"
+    SIERPINSKI = "sierpinski"
+    JULIA = "julia"
+    CANTOR = "cantor"
+    DRAGON_CURVE = "dragon_curve"
+
+class FractalPatternGenerator:
+    """
+    Gerador de padrões fractais para definir as regras de conexão
+    entre neurônios na FractalBrainNet.
+    """
+    
+    @staticmethod
+    def mandelbrot_connectivity(width: int, height: int, max_iter: int = 100) -> torch.Tensor:
+        """
+        Gera matriz de conectividade baseada no conjunto de Mandelbrot.
+        Valores mais altos indicam conexões mais fortes.
+        """
+        x = torch.linspace(-2.5, 1.5, width)
+        y = torch.linspace(-1.5, 1.5, height)
+        X, Y = torch.meshgrid(x, y, indexing='ij')
+        c = X + 1j * Y
+        z = torch.zeros_like(c)
+        
+        connectivity = torch.zeros(width, height)
+        
+        for i in range(max_iter):
+            mask = torch.abs(z) <= 2
+            z[mask] = z[mask] ** 2 + c[mask]
+            connectivity[mask] += 1
+        
+        # Normalizar para [0, 1]
+        connectivity = connectivity / max_iter
+        return connectivity
+    
+    @staticmethod
+    def sierpinski_connectivity(size: int, iterations: int = 5) -> torch.Tensor:
+        """
+        Gera matriz de conectividade baseada no triângulo de Sierpinski.
+        """
+        pattern = torch.zeros(size, size)
+        pattern[0, size//2] = 1.0
+        
+        for _ in range(iterations):
+            new_pattern = torch.zeros_like(pattern)
+            for i in range(size-1):
+                for j in range(size-1):
+                    if pattern[i, j] > 0:
+                        # Regra do triângulo de Sierpinski
+                        if i+1 < size and j > 0:
+                            new_pattern[i+1, j-1] = 1.0
+                        if i+1 < size and j+1 < size:
+                            new_pattern[i+1, j+1] = 1.0
+            pattern = torch.maximum(pattern, new_pattern)
+        
+        return pattern
+    
+    @staticmethod
+    def julia_connectivity(width: int, height: int, c_real: float = -0.7, 
+                          c_imag: float = 0.27015, max_iter: int = 100) -> torch.Tensor:
+        """
+        Gera matriz de conectividade baseada no conjunto de Julia.
+        """
+        x = torch.linspace(-2, 2, width)
+        y = torch.linspace(-2, 2, height)
+        X, Y = torch.meshgrid(x, y, indexing='ij')
+        z = X + 1j * Y
+        c = complex(c_real, c_imag)
+        
+        connectivity = torch.zeros(width, height)
+        
+        for i in range(max_iter):
+            mask = torch.abs(z) <= 2
+            z[mask] = z[mask] ** 2 + c
+            connectivity[mask] += 1
+        
+        connectivity = connectivity / max_iter
+        return connectivity
+
+class CerebralDynamicsModule(nn.Module):
+    """
+    Módulo que simula dinâmicas cerebrais através de processamento
+    distribuído e paralelo, inspirado na organização hierárquica do cérebro.
+    """
+    
+    def __init__(self, channels: int, fractal_pattern: torch.Tensor):
+        super().__init__()
+        self.channels = channels
+        self.fractal_pattern = nn.Parameter(fractal_pattern, requires_grad=False)
+        
+        # Múltiplas escalas de processamento (simulando diferentes frequências cerebrais)
+        self.alpha_processing = nn.Conv2d(channels, channels//4, 1)  # 8-12 Hz
+        self.beta_processing = nn.Conv2d(channels, channels//4, 1)   # 13-30 Hz
+        self.gamma_processing = nn.Conv2d(channels, channels//4, 1)  # 30-100 Hz
+        self.theta_processing = nn.Conv2d(channels, channels//4, 1)  # 4-8 Hz
+        
+        # Integração das diferentes escalas
+        self.integration = nn.Conv2d(channels, channels, 1)
+        self.normalization = nn.LayerNorm([channels])
+        
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        batch_size, channels, height, width = x.shape
+        
+        # Aplicar padrão fractal como máscara de atenção
+        if self.fractal_pattern.shape[-2:] != (height, width):
+            fractal_mask = F.interpolate(
+                self.fractal_pattern.unsqueeze(0).unsqueeze(0), 
+                size=(height, width), mode='bilinear', align_corners=False
+            ).squeeze()
+        else:
+            fractal_mask = self.fractal_pattern
+        
+        # Processamento em múltiplas escalas (simulando bandas de frequência cerebral)
+        alpha = self.alpha_processing(x) * fractal_mask.unsqueeze(0).unsqueeze(0)
+        beta = self.beta_processing(x) * (1 - fractal_mask.unsqueeze(0).unsqueeze(0))
+        gamma = self.gamma_processing(x) * fractal_mask.unsqueeze(0).unsqueeze(0) * 0.5
+        theta = self.theta_processing(x) * torch.sin(fractal_mask * math.pi).unsqueeze(0).unsqueeze(0)
+        
+        # Combinar diferentes escalas
+        combined = torch.cat([alpha, beta, gamma, theta], dim=1)
+        integrated = self.integration(combined)
+        
+        # Normalização adaptativa
+        integrated = integrated.permute(0, 2, 3, 1)
+        integrated = self.normalization(integrated)
+        integrated = integrated.permute(0, 3, 1, 2)
+        
+        return integrated + x  # Conexão residual
+
+class FractalNeuralBlock(nn.Module):
+    """
+    Bloco neural fractal que implementa a regra de expansão fractal
+    com dinâmicas cerebrais integradas.
+    """
+    
+    def __init__(self, level: int, in_channels: int, out_channels: int,
+                 fractal_pattern: torch.Tensor, drop_path_prob: float = 0.1):
+        super().__init__()
+        self.level = level
+        
+        if level == 1:
+            # Caso base com dinâmicas cerebrais
+            self.base_conv = nn.Conv2d(in_channels, out_channels, 3, padding=1)
+            self.cerebral_dynamics = CerebralDynamicsModule(out_channels, fractal_pattern)
+            self.activation = nn.GELU()  # GELU para maior expressividade
+            self.norm = nn.BatchNorm2d(out_channels)
+        else:
+            # Estrutura recursiva fractal
+            self.deep_branch = nn.Sequential(
+                FractalNeuralBlock(level-1, in_channels, out_channels, fractal_pattern, drop_path_prob),
+                FractalNeuralBlock(level-1, out_channels, out_channels, fractal_pattern, drop_path_prob)
+            )
+            
+            self.shallow_branch = nn.Sequential(
+                nn.Conv2d(in_channels, out_channels, 3, padding=1),
+                CerebralDynamicsModule(out_channels, fractal_pattern),
+                nn.BatchNorm2d(out_channels),
+                nn.GELU()
+            )
+            
+            # Mecanismo de atenção fractal
+            self.fractal_attention = nn.Sequential(
+                nn.Conv2d(out_channels * 2, out_channels // 4, 1),
+                nn.GELU(),
+                nn.Conv2d(out_channels // 4, 2, 1),
+                nn.Sigmoid()
+            )
+            
+        self.drop_path = nn.Dropout2d(drop_path_prob) if drop_path_prob > 0 else nn.Identity()
+    
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        if self.level == 1:
+            out = self.base_conv(x)
+            out = self.norm(out)
+            out = self.cerebral_dynamics(out)
+            out = self.activation(out)
+            return self.drop_path(out)
+        else:
+            # Processamento em ramos paralelos
+            deep_out = self.deep_branch(x)
+            shallow_out = self.shallow_branch(x)
+            
+            # Mecanismo de atenção para combinar ramos
+            combined = torch.cat([deep_out, shallow_out], dim=1)
+            attention_weights = self.fractal_attention(combined)
+            
+            # Combinar com pesos adaptativos
+            alpha, beta = attention_weights.chunk(2, dim=1)
+            result = alpha * deep_out + beta * shallow_out
+            
+            return self.drop_path(result)
+
+class AdaptiveScaleProcessor(nn.Module):
+    """
+    Processador adaptativo que opera em múltiplas escalas,
+    simulando a capacidade do cérebro de processar informações
+    em diferentes níveis de abstração simultaneamente.
+    """
+    
+    def __init__(self, channels: int):
+        super().__init__()
+        self.channels = channels
+        
+        # Diferentes escalas de processamento
+        self.local_processor = nn.Conv2d(channels, channels, 1)
+        self.regional_processor = nn.Conv2d(channels, channels, 3, padding=1)
+        self.global_processor = nn.Conv2d(channels, channels, 5, padding=2)
+        
+        # Integração adaptativa
+        self.scale_fusion = nn.Sequential(
+            nn.Conv2d(channels * 3, channels, 1),
+            nn.BatchNorm2d(channels),
+            nn.GELU()
+        )
+        
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        local = self.local_processor(x)
+        regional = self.regional_processor(x)
+        global_proc = self.global_processor(x)
+        
+        # Combinar escalas
+        multi_scale = torch.cat([local, regional, global_proc], dim=1)
+        fused = self.scale_fusion(multi_scale)
+        
+        return fused + x
+
+class FractalBrainNet(nn.Module):
+    """
+    FractalBrainNet: Rede neural que combina a profundidade das redes profundas
+    com a complexidade e elegância dos fractais, capaz de emular dinâmicas cerebrais
+    através de estruturas hierárquicas e auto-similares.
+    
+    Baseada no artigo de Jose R. F. Junior (2024).
+    """
+    
+    def __init__(self, 
+                 num_classes: int = 10,
+                 in_channels: int = 3,
+                 fractal_levels: List[int] = [2, 3, 4, 5],
+                 base_channels: int = 64,
+                 fractal_pattern_type: FractalPatternType = FractalPatternType.MANDELBROT,
+                 pattern_resolution: int = 32,
+                 drop_path_prob: float = 0.15,
+                 enable_continuous_learning: bool = True):
+        
+        super().__init__()
+        
+        self.num_classes = num_classes
+        self.fractal_levels = fractal_levels
+        self.enable_continuous_learning = enable_continuous_learning
+        
+        # Gerar padrão fractal base
+        self.fractal_pattern = self._generate_fractal_pattern(
+            fractal_pattern_type, pattern_resolution
+        )
+        
+        # Camada de entrada adaptativa
+        self.stem = nn.Sequential(
+            nn.Conv2d(in_channels, base_channels, 7, stride=2, padding=3),
+            nn.BatchNorm2d(base_channels),
+            nn.GELU(),
+            AdaptiveScaleProcessor(base_channels)
+        )
+        
+        # Blocos fractais neurais hierárquicos
+        self.fractal_stages = nn.ModuleList()
+        current_channels = base_channels
+        
+        for i, level in enumerate(fractal_levels):
+            # Aumentar canais progressivamente
+            stage_channels = base_channels * (2 ** min(i, 4))
+            
+            # Bloco fractal principal
+            fractal_block = FractalNeuralBlock(
+                level, current_channels, stage_channels, 
+                self.fractal_pattern, drop_path_prob
+            )
+            
+            # Processador multi-escala
+            scale_processor = AdaptiveScaleProcessor(stage_channels)
+            
+            # Pooling adaptativo
+            if i < len(fractal_levels) - 1:
+                pooling = nn.Sequential(
+                    nn.Conv2d(stage_channels, stage_channels, 3, stride=2, padding=1),
+                    nn.BatchNorm2d(stage_channels),
+                    nn.GELU()
+                )
+            else:
+                pooling = nn.Identity()
+            
+            self.fractal_stages.append(nn.Sequential(
+                fractal_block,
+                scale_processor,
+                pooling
+            ))
+            
+            current_channels = stage_channels
+        
+        # Sistema de atenção global inspirado na atenção cerebral
+        self.global_attention = nn.MultiheadAttention(
+            current_channels, num_heads=8, batch_first=True
+        )
+        
+        # Cabeça de classificação com aprendizado contínuo
+        self.adaptive_pool = nn.AdaptiveAvgPool2d((1, 1))
+        self.classifier = nn.Sequential(
+            nn.Dropout(0.2),
+            nn.Linear(current_channels, current_channels // 2),
+            nn.GELU(),
+            nn.Dropout(0.1),
+            nn.Linear(current_channels // 2, num_classes)
+        )
+        
+        # Módulo de meta-aprendizado para adaptação contínua
+        if enable_continuous_learning:
+            self.meta_learner = nn.Sequential(
+                nn.Linear(current_channels, current_channels // 4),
+                nn.GELU(),
+                nn.Linear(current_channels // 4, current_channels)
+            )
+        
+        self._initialize_weights()
+    
+    def _generate_fractal_pattern(self, pattern_type: FractalPatternType, 
+                                 resolution: int) -> torch.Tensor:
+        """Gera o padrão fractal base para a rede."""
+        if pattern_type == FractalPatternType.MANDELBROT:
+            return FractalPatternGenerator.mandelbrot_connectivity(resolution, resolution)
+        elif pattern_type == FractalPatternType.SIERPINSKI:
+            return FractalPatternGenerator.sierpinski_connectivity(resolution)
+        elif pattern_type == FractalPatternType.JULIA:
+            return FractalPatternGenerator.julia_connectivity(resolution, resolution)
+        else:
+            # Padrão padrão (Mandelbrot)
+            return FractalPatternGenerator.mandelbrot_connectivity(resolution, resolution)
+    
+    def _initialize_weights(self):
+        """Inicialização de pesos inspirada na neuroplasticidade."""
+        for m in self.modules():
+            if isinstance(m, nn.Conv2d):
+                # Inicialização He com variação fractal
+                nn.init.kaiming_normal_(m.weight, mode='fan_out', nonlinearity='relu')
+                if m.bias is not None:
+                    nn.init.constant_(m.bias, 0)
+            elif isinstance(m, (nn.BatchNorm2d, nn.LayerNorm)):
+                nn.init.constant_(m.weight, 1.0)
+                nn.init.constant_(m.bias, 0.0)
+            elif isinstance(m, nn.Linear):
+                nn.init.trunc_normal_(m.weight, std=0.02)
+                if m.bias is not None:
+                    nn.init.constant_(m.bias, 0)
+    
+    def forward(self, x: torch.Tensor, 
+                return_attention_maps: bool = False) -> torch.Tensor:
+        """
+        Forward pass com processamento hierárquico e dinâmicas cerebrais.
+        """
+        # Extração inicial de características
+        x = self.stem(x)
+        
+        attention_maps = []
+        
+        # Processamento através dos estágios fractais
+        for stage in self.fractal_stages:
+            x = stage(x)
+            
+            if return_attention_maps:
+                # Capturar mapas de atenção para análise
+                attention_map = torch.mean(x, dim=1, keepdim=True)
+                attention_maps.append(attention_map)
+        
+        # Pooling adaptativo global
+        pooled = self.adaptive_pool(x)
+        features = pooled.flatten(1)
+        
+        # Aplicar atenção global se habilitada
+        if hasattr(self, 'global_attention'):
+            # Reformatar para atenção multi-cabeça
+            attn_input = features.unsqueeze(1)
+            attended, _ = self.global_attention(attn_input, attn_input, attn_input)
+            features = attended.squeeze(1)
+        
+        # Meta-aprendizado para adaptação contínua
+        if self.enable_continuous_learning and hasattr(self, 'meta_learner'):
+            meta_features = self.meta_learner(features)
+            features = features + 0.1 * meta_features  # Residual meta-learning
+        
+        # Classificação final
+        output = self.classifier(features)
+        
+        if return_attention_maps:
+            return output, attention_maps
+        return output
+    
+    def analyze_fractal_patterns(self, x: torch.Tensor) -> Dict[str, torch.Tensor]:
+        """
+        Analisa os padrões emergentes gerados pela estrutura fractal,
+        conforme mencionado na metodologia do artigo.
+        """
+        self.eval()
+        with torch.no_grad():
+            _, attention_maps = self.forward(x, return_attention_maps=True)
+            
+            analysis = {
+                'fractal_pattern': self.fractal_pattern,
+                'attention_maps': attention_maps,
+                'pattern_complexity': self._compute_pattern_complexity(attention_maps),
+                'hierarchical_organization': self._analyze_hierarchical_organization(attention_maps)
+            }
+            
+        return analysis
+    
+    def _compute_pattern_complexity(self, attention_maps: List[torch.Tensor]) -> List[float]:
+        """Computa a complexidade dos padrões emergentes."""
+        complexities = []
+        for attention_map in attention_maps:
+            # Usar entropia como medida de complexidade
+            flat_map = attention_map.flatten()
+            prob_dist = F.softmax(flat_map, dim=0)
+            entropy = -torch.sum(prob_dist * torch.log(prob_dist + 1e-8))
+            complexities.append(entropy.item())
+        return complexities
+    
+    def _analyze_hierarchical_organization(self, attention_maps: List[torch.Tensor]) -> Dict[str, float]:
+        """Analisa a organização hierárquica dos padrões."""
+        if len(attention_maps) < 2:
+            return {'correlation': 0.0, 'hierarchy_score': 0.0}
+        
+        # Correlação entre níveis hierárquicos
+        correlations = []
+        for i in range(len(attention_maps) - 1):
+            map1 = attention_maps[i].flatten()
+            map2 = F.interpolate(attention_maps[i+1], size=attention_maps[i].shape[-2:], 
+                               mode='bilinear', align_corners=False).flatten()
+            correlation = torch.corrcoef(torch.stack([map1, map2]))[0, 1]
+            correlations.append(correlation.item())
+        
+        avg_correlation = sum(correlations) / len(correlations)
+        hierarchy_score = 1.0 - avg_correlation  # Maior diversidade = maior hierarquia
+        
+        return {
+            'correlation': avg_correlation,
+            'hierarchy_score': hierarchy_score
+        }
+
+# Função para criar modelos FractalBrainNet pré-configurados
+def create_fractal_brain_net(model_size: str = 'medium',
+                           num_classes: int = 10,
+                           fractal_pattern: FractalPatternType = FractalPatternType.MANDELBROT) -> FractalBrainNet:
+    """
+    Cria modelos FractalBrainNet pré-configurados inspirados no artigo de Jose R. F. Junior.
+    
+    Args:
+        model_size: 'small', 'medium', 'large', 'xlarge'
+        num_classes: número de classes para classificação
+        fractal_pattern: tipo de padrão fractal a ser usado
+    """
+    configs = {
+        'small': {
+            'fractal_levels': [2, 3],
+            'base_channels': 32,
+            'pattern_resolution': 16
+        },
+        'medium': {
+            'fractal_levels': [2, 3, 4],
+            'base_channels': 64,
+            'pattern_resolution': 32
+        },
+        'large': {
+            'fractal_levels': [2, 3, 4, 5],
+            'base_channels': 96,
+            'pattern_resolution': 64
+        },
+        'xlarge': {
+            'fractal_levels': [3, 4, 5, 6],
+            'base_channels': 128,
+            'pattern_resolution': 128
+        }
+    }
+    
+    config = configs.get(model_size, configs['medium'])
+    
+    return FractalBrainNet(
+        num_classes=num_classes,
+        fractal_levels=config['fractal_levels'],
+        base_channels=config['base_channels'],
+        fractal_pattern_type=fractal_pattern,
+        pattern_resolution=config['pattern_resolution']
+    )
+
+# Demonstração e teste
+if __name__ == "__main__":
+    print("=== FractalBrainNet - Implementação Avançada ===")
+    print("Baseada no artigo de Jose R. F. Junior (2024)")
+    print()
+    
+    # Criar modelo com diferentes padrões fractais
+    models = {
+        'Mandelbrot': create_fractal_brain_net('medium', 10, FractalPatternType.MANDELBROT),
+        'Sierpinski': create_fractal_brain_net('medium', 10, FractalPatternType.SIERPINSKI),
+        'Julia': create_fractal_brain_net('medium', 10, FractalPatternType.JULIA)
+    }
+    
+    # Teste com entrada dummy
+    dummy_input = torch.randn(2, 3, 64, 64)
+    
+    for name, model in models.items():
+        print(f"\n=== Modelo com padrão {name} ===")
+        
+        # Forward pass normal
+        output = model(dummy_input)
+        print(f"Output shape: {output.shape}")
+        
+        # Análise de padrões fractais emergentes
+        analysis = model.analyze_fractal_patterns(dummy_input)
+        print(f"Níveis de atenção capturados: {len(analysis['attention_maps'])}")
+        print(f"Complexidade dos padrões: {analysis['pattern_complexity']}")
+        print(f"Organização hierárquica: {analysis['hierarchical_organization']}")
+        
+        # Estatísticas do modelo
+        total_params = sum(p.numel() for p in model.parameters())
+        print(f"Parâmetros totais: {total_params:,}")
+    
+    print("\n=== FractalBrainNet criada com sucesso! ===")
+    print("Esta implementação incorpora:")
+    print("- Padrões fractais (Mandelbrot, Sierpinski, Julia)")
+    print("- Simulação de dinâmicas cerebrais")
+    print("- Processamento hierárquico e multi-escala")
+    print("- Mecanismos de atenção inspirados no cérebro")
+    print("- Capacidade de aprendizado contínuo")
+    print("- Análise de padrões emergentes")
+
+
+"""
+# Criar modelo com padrão Mandelbrot
+model = create_fractal_brain_net('large', num_classes=1000, 
+                                fractal_pattern=FractalPatternType.MANDELBROT)
+
+# Forward pass normal
+output = model(input_tensor)
+
+# Análise de padrões emergentes
+analysis = model.analyze_fractal_patterns(input_tensor)
+print("Complexidade dos padrões:", analysis['pattern_complexity'])
+print("Organização hierárquica:", analysis['hierarchical_organization'])
+"""