Visual complexity refers to the intricate and detailed visual representation of complex systems, networks, and data. It involves using various visual elements to map and understand the relationships, patterns, and structures within complex information.

The main purpose of visual complexity in information design is to develop effective ways to visually represent complex systems and data. This aids in understanding, analyzing, and communicating intricate information across various disciplines, such as biology, social networks, and the World Wide Web.

Key characteristics of complex systems that can be visually represented include:

1. Feedback
2. Emergence
3. Self-organization
4. Non-linearity
5. Adaptation
6. Nested systems
7. Multiple scales

Visual variables that can be manipulated to represent complex data include:

1. Position
2. Size
3. Shape
4. Color
5. Texture
6. Orientation
7. Connection (lines or edges between elements)

Challenges in visualizing complex systems or data include:

1. Balancing detail and clarity
2. Representing multiple dimensions or scales
3. Showing dynamic or temporal aspects
4. Avoiding information overload
5. Ensuring the visualization is intuitive and understandable
6. Dealing with large datasets

Network visualization is the process of visually representing the structure, connections, and relationships within complex networks. It's important in visual complexity because it helps reveal patterns, clusters, and key nodes or hubs within systems, aiding in the understanding of complex interconnected structures.

Visual complexity is relevant in numerous fields, including:

1. Biology (e.g., visualizing ecosystems or cellular networks)
2. Social network analysis
3. Computer science and the World Wide Web
4. Urban planning and transportation systems
5. Economics and financial markets
6. Climate science and environmental systems
7. Neuroscience (brain connectivity)

Common tools for creating visual complexity representations often include:

1. Gephi
2. Cytoscape
3. D3.js
4. Processing
5. Tableau
6. R with ggplot2
7. Python with matplotlib or seaborn

The effectiveness of a visual complexity representation can be evaluated by:

1. Assessing its ability to convey information quickly and accurately
2. Checking if it facilitates the extraction of patterns and insights
3. Evaluating its aesthetic appeal and engagement
4. Testing user comprehension and interpretation
5. Measuring its ability to support decision-making or problem-solving in the relevant domain

Emerging trends and future directions in visual complexity include:

1. Integration of interactive and dynamic visualizations
2. Use of virtual and augmented reality for immersive data exploration
3. Application of machine learning and AI for pattern recognition and visualization
4. Development of standardized visual languages for complexity
5. Exploration of multi-sensory representations of complex data
6. Improved techniques for visualizing temporal and spatial dynamics in complex systems