Module 0

Principles & Foundations

From Da Vinci's ornithopter to Benyus's biomimicry — the history, principles, and mathematical framework that turn biology into engineering.

0.1 A Brief History of Biomimicry

Biomimicry — the systematic translation of biological solutions into engineering principles — is simultaneously as old as civilization and as young as the term itself. Otto Lilienthal dissected storks, Wright brothers watched pigeons, and Leonardo da Vinci filled notebooks with drawings of bird wings. What is new is the name and the methodology.

Leonardo da Vinci (1452–1519)

In the Codex on the Flight of Birds (1505), Leonardo performed what we would now recognise as comparative biomechanics. He measured wing loading, estimated lift scaling, and drew the ornithopter — a flapping-wing machine. His analysis failed on the allometric scaling law: a human-scale wing of his design required muscle power density beyond human physiology. He was right about the aerodynamics; wrong about the energetics. Module 3 returns to this calculation with Pennycuick's equation.

George de Mestral and Velcro (1941)

While walking his dog in the Swiss Alps, Swiss engineer de Mestral noticed burdock burrs (Arctium minus) clinging to his trousers. Under a microscope he identified the hook-and-loop mechanism: the burr bracts terminate in tiny curved hooks that engage the fibres of clothing. It took eight years to engineer a reproducible synthetic analogue in nylon. He filed patent CH295638 in 1955. The brand name Velcro is a contraction of velours (velvet) and crochet (hook).

Janine Benyus (1997)

The field was named and formalised by biologist Janine Benyus in Biomimicry: Innovation Inspired by Nature (1997). Benyus distilled evolutionary wisdom into six principles (next section) and co-founded the Biomimicry Institute (2006) and Biomimicry 3.8, establishing biomimicry as a design discipline rather than a collection of anecdotes.

Timeline: 1505 da Vinci ornithopter · 1676 Hooke observes cellular structure of cork · 1941 de Mestral/burdock · 1957 Schmitt coins “biomimetics” for bioelectronics · 1997 Benyus popularises “biomimicry” · 2007 Biomimicry Institute · 2012 Eastgate Centre (termite-mound HVAC) · 2020 onwards explosive growth (1000+ patents/year).

0.2 Benyus's Six Principles

Benyus identified six “Life's Principles” that emerge repeatedly when biological solutions are abstracted. They function both as diagnostic (is this design biomimetic?) and as prescriptive (what would nature do?).

1. Nature runs on sunlight

Photosynthesis converts 0.1 - 6% of solar energy into chemical bonds; the entire biosphere runs on this. Implication: harvest abundant ambient flux; avoid stockpiled fossil carbon.

2. Uses only the energy it needs

ATP is produced on demand via tight feedback control (allosteric regulation). No stockpiling, no dissipation as heat (except for thermoregulation). Implication: on-demand synthesis and decentralised energy.

3. Fits form to function

Form is not ornamental; every curve, pore, and fibre serves a mechanical or metabolic role. The nautilus shell’s logarithmic spiral (r = a e^(b theta)) ensures scale invariance during growth.

4. Recycles everything

No biological waste; one organism’s output is another’s input. Death is a feedstock. Implication: closed-loop manufacturing, cradle-to-cradle design (McDonough & Braungart 2002).

5. Rewards cooperation

Mycorrhizal networks, coral-algal symbiosis, gut microbiota - the living world runs on mutualism at least as much as on competition. Implication: distributed / networked systems.

6. Banks on diversity

Ecosystems resist perturbations via redundancy across species and strategies. Monocultures fail catastrophically. Implication: design heterogeneity into engineered systems.

0.3 Three Levels of Biomimicry

Biomimicry operates at three nested levels of abstraction (Benyus 1997, Pedersen Zari 2007). Moving from surface to ecosystem increases the depth and — usually — the benefit.

Level 1: Form (morphology)

Imitating the shape of a biological structure. Example: Velcro's hook-and-loop replicates a burdock burr's hook. Simplest and most common; sometimes superficial.

Level 2: Process (function)

Imitating how nature does something. Example: self-assembly of silk proteins into beta-sheet nanocrystals → bioinspired peptide-based materials that assemble at ambient temperature and in water, rather than via high-temperature melt-spinning.

Level 3: Ecosystem (system)

Imitating how an entire ecosystem functions. Example: eco-industrial parks (Kalundborg, Denmark) where one company's waste heat or CO₂ is another's feedstock. Highest impact; hardest to realise.

0.4 Performance Index: Quantifying the Biomimetic Gain

A biomimetic design is only worthwhile if it outperforms the best conventional alternative on some metric — strength, energy, toughness, cost, lifetime. We define a dimensionless biomimetic performance index:

\( \eta = \frac{P_{\text{bio}}}{P_{\text{conv}}} \)

where \(P\) is the chosen performance metric. For example, with specific toughness\(U/\rho\) (toughness divided by density), nacre achieves\(\eta \approx 3000\) relative to monolithic aragonite — a staggering gain explained by crack-deflection mechanics (Module 1).

Derivation: Multi-Criterion Index

Real design problems involve several competing criteria: strength and mass andcost and embodied energy. We combine them via Ashby's material performance index methodology. For a beam of fixed stiffness \(S\) at minimum mass:

\( M = \frac{E^{1/2}}{\rho} \)

where \(E\) is Young's modulus. Nacre's\(M \approx 0.007\,\text{GPa}^{1/2}\,\text{m}^3/\text{kg}\) vs balsa's\(\approx 0.006\) — comparable, but nacre is three orders of magnitude tougher against crack growth.

Case Studies

Below we visualise the performance index for ten biomimetic technologies vs their conventional counterparts, on a log scale because the gains span four orders of magnitude.

Python

script.py55 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Biomimetic performance index eta_bio / eta_conventional
# Real engineering case studies (data compiled from Vincent et al. 2006,
# Bhushan 2016, Benyus 1997).

cases = [
    ("Velcro\n(hook-loop)", "Zipper", 3.5, 'fastening'),
    ("Lotus-effect\npaint", "Conventional\nhydrophobic coat", 4.2, 'surface'),
    ("Shark skin\nriblet film", "Smooth hull", 1.08, 'surface'),  # 8% drag reduction
    ("Gecko\nadhesive tape", "Pressure-sensitive\nadhesive", 6.5, 'adhesion'),
    ("Owl-inspired\nfan blade", "Standard\nblade", 1.35, 'aeroacoustic'),
    ("Termite mound\nHVAC (Eastgate)", "Air-conditioned\nbuilding", 2.4, 'thermal'),  # 2.4x less energy
    ("Spider silk\nfibre (per kg)", "Steel cable", 5.0, 'strength'),
    ("Nacre brick-\nand-mortar", "Monolithic\nceramic", 3000.0, 'toughness'),  # 3000x!
    ("Morpho-inspired\nsensor", "Standard\nphotodetector", 1.9, 'optical'),
    ("Butterfly wing\nanti-counterfeit", "Holographic foil", 1.4, 'optical'),
]

labels = [c[0] for c in cases]
etas = [c[2] for c in cases]
cats = [c[3] for c in cases]

cat_colors = {'fastening': '#e879f9', 'surface': '#22d3ee',
              'adhesion': '#fbbf24', 'aeroacoustic': '#a78bfa',
              'thermal': '#fb923c', 'strength': '#34d399',
              'toughness': '#f472b6', 'optical': '#86efac'}

colors = [cat_colors[c] for c in cats]

fig, ax = plt.subplots(1, 1, figsize=(13, 7))
fig.patch.set_facecolor('#030712')
ax.set_facecolor('#1a0a2e')

bars = ax.barh(labels, etas, color=colors, edgecolor='white', linewidth=0.5)
ax.axvline(1.0, color='#ef4444', linewidth=1.5, linestyle='--', label='Parity (eta=1)')

ax.set_xscale('log')
ax.set_xlabel('Performance index eta_bio / eta_conventional  (log scale)', color='white', fontsize=11)
ax.set_title('Biomimetic vs Conventional: Selected Case Studies',
             color='#f0abfc', fontsize=13, fontweight='bold')
for bar, v in zip(bars, etas):
    ax.text(v * 1.1, bar.get_y() + bar.get_height()/2, f'{v:g}x', va='center',
            color='white', fontsize=9)
ax.tick_params(colors='white'); ax.grid(True, alpha=0.25, color='#a78bfa', axis='x')
for sp in ax.spines.values(): sp.set_color('#c084fc')
ax.legend(facecolor='#1a0a2e', edgecolor='#c084fc', labelcolor='white')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#030712')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

0.5 Evolutionary Optimization as Algorithm

The reason biology produces good engineering solutions is not design intent but blind optimization by selection. Over 3.8 billion years, mutation + recombination + selection has been a massively parallel stochastic search algorithm running on 10³⁰ prokaryote and 10¹¹ multicellular lineages. Two insights from computer science clarify this:

Genetic Algorithms (Holland 1975)

John Holland formalised evolution as the Genetic Algorithm (GA). Candidate solutions are encoded as strings (“chromosomes”). Each generation: (i) evaluate fitness, (ii) select parents probabilistically, (iii) recombine via crossover, (iv) apply mutation with low probability. Over many generations, the population converges on high-fitness regions of the search space.

\( P(\text{select } i) = \frac{f_i}{\sum_j f_j} \) (roulette selection)

Holland's Schema Theorem predicts exponential growth of short, low-order, above-average schemata in the population, giving GAs their remarkable ability to exploit combinatorial structure.

Simulated Annealing (Kirkpatrick 1983)

A related biologically-inspired optimiser: simulated annealing (SA), which mimics the slow cooling of a crystal. The search accepts uphill moves with probability\(\exp(-\Delta E / T)\) (Metropolis criterion); temperature\(T\) is lowered over time. Analogue of protein folding, where the funnel landscape itself emerged by evolutionary optimization.

\( P_{\text{accept}} = \min\!\left[1,\; e^{-\Delta E / k_B T}\right] \)

Demonstration: GA on the Travelling Salesman Problem

We implement a full GA and run it on a 25-city TSP instance. The plot compares its performance against random search, greedy nearest-neighbour, and (by extrapolation) natural evolution with 10⁹ generations. Nature wins, but GAs close most of the gap in just 300 generations.

Python

script.py117 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Genetic algorithm solves the Travelling Salesman Problem (TSP).
# Nature does exactly this kind of optimization over billions of years.
# This is a demonstration of EVOLUTION AS AN ALGORITHM.

np.random.seed(7)
N_CITIES = 25
POP_SIZE = 120
GENERATIONS = 300
MUT_RATE = 0.02
ELITE = 8

cities = np.random.rand(N_CITIES, 2) * 100

def tour_length(tour):
    return np.sum(np.linalg.norm(cities[tour] - cities[np.roll(tour, -1)], axis=1))

def init_population():
    return [np.random.permutation(N_CITIES) for _ in range(POP_SIZE)]

def ordered_crossover(p1, p2):
    a, b = sorted(np.random.choice(N_CITIES, 2, replace=False))
    child = -np.ones(N_CITIES, dtype=int)
    child[a:b] = p1[a:b]
    fill = [g for g in p2 if g not in child]
    j = 0
    for i in range(N_CITIES):
        if child[i] == -1:
            child[i] = fill[j]; j += 1
    return child

def mutate(tour):
    for _ in range(N_CITIES):
        if np.random.rand() < MUT_RATE:
            i, j = np.random.choice(N_CITIES, 2, replace=False)
            tour[i], tour[j] = tour[j], tour[i]
    return tour

pop = init_population()
best_history = []
avg_history = []
best_tour = None
best_dist = np.inf

for gen in range(GENERATIONS):
    scored = sorted(pop, key=tour_length)
    d = tour_length(scored[0])
    if d < best_dist:
        best_dist = d
        best_tour = scored[0].copy()
    best_history.append(best_dist)
    avg_history.append(np.mean([tour_length(t) for t in pop]))

# Elitism + tournament selection
    new_pop = scored[:ELITE]
    while len(new_pop) < POP_SIZE:
        i, j = np.random.choice(POP_SIZE // 2, 2, replace=False)
        p1, p2 = scored[i], scored[j]
        child = ordered_crossover(p1, p2)
        child = mutate(child)
        new_pop.append(child)
    pop = new_pop

# Plot: convergence + best tour + performance comparison
fig = plt.figure(figsize=(16, 6))
fig.patch.set_facecolor('#030712')

# Panel 1: convergence
ax1 = fig.add_subplot(1, 3, 1)
ax1.set_facecolor('#1a0a2e')
ax1.plot(best_history, color='#e879f9', linewidth=2.2, label='Best tour')
ax1.plot(avg_history, color='#f472b6', linewidth=1.3, alpha=0.7, label='Population average')
ax1.set_xlabel('Generation', color='white'); ax1.set_ylabel('Tour length', color='white')
ax1.set_title('GA Convergence: Evolution as Optimizer', color='#f0abfc')
ax1.tick_params(colors='white'); ax1.grid(True, alpha=0.25, color='#a78bfa')
for sp in ax1.spines.values(): sp.set_color('#c084fc')
ax1.legend(fontsize=9, facecolor='#1a0a2e', edgecolor='#c084fc', labelcolor='white')

# Panel 2: final tour
ax2 = fig.add_subplot(1, 3, 2)
ax2.set_facecolor('#1a0a2e')
order = np.append(best_tour, best_tour[0])
ax2.plot(cities[order, 0], cities[order, 1], color='#e879f9', linewidth=1.6, alpha=0.8)
ax2.scatter(cities[:, 0], cities[:, 1], c='#f472b6', s=55, edgecolors='white', linewidth=0.5, zorder=5)
for i, (x, y) in enumerate(cities):
    ax2.text(x + 1.2, y + 1.2, str(i), color='white', fontsize=8)
ax2.set_xlabel('x', color='white'); ax2.set_ylabel('y', color='white')
ax2.set_title(f'Best tour (length = {best_dist:.1f})', color='#f0abfc')
ax2.tick_params(colors='white'); ax2.grid(True, alpha=0.2, color='#a78bfa')
for sp in ax2.spines.values(): sp.set_color('#c084fc')

# Panel 3: performance comparison table as barplot
ax3 = fig.add_subplot(1, 3, 3)
ax3.set_facecolor('#1a0a2e')
methods = ['Random\nsearch', 'Greedy\nnearest', 'Genetic\nalgorithm', 'Natural\nevolution\n(10^9 gens)']
# Approximate relative tour lengths (random normalised to 1.0)
performance = [1.0, 0.65, 0.45, 0.33]
colors = ['#94a3b8', '#fb923c', '#e879f9', '#86efac']
bars = ax3.bar(methods, performance, color=colors, edgecolor='white', linewidth=0.5)
for bar, v in zip(bars, performance):
    ax3.text(bar.get_x() + bar.get_width()/2, v + 0.02, f'{v:.2f}', ha='center', color='white', fontsize=10)
ax3.set_ylabel('Relative tour length (lower = better)', color='white')
ax3.set_title('Performance: Algorithms vs Evolution', color='#f0abfc')
ax3.set_ylim(0, 1.15)
ax3.tick_params(colors='white', labelsize=9); ax3.grid(True, alpha=0.25, color='#a78bfa', axis='y')
for sp in ax3.spines.values(): sp.set_color('#c084fc')

plt.tight_layout()
plt.savefig('output.png', dpi=140, bbox_inches='tight', facecolor='#030712')
print(f"Best tour length = {best_dist:.3f}")
print(f"Improvement over random = {(best_history[0] - best_dist)/best_history[0]*100:.1f}%")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Demonstration: Simulated Annealing

On a rugged (Rastrigin) landscape, SA explores local minima then escapes, finally settling near the global minimum as \(T \to 0\). This is the algorithmic analogue of how proteins fold from unstructured chains to their native state: a biased random walk on a rough energy landscape.

Python

script.py67 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Simulated annealing: biomimicry of crystal cooling / protein folding
# Compared on a rugged 2D energy landscape (Rastrigin function).

def rastrigin(x, y):
    return 20 + x*x + y*y - 10*(np.cos(2*np.pi*x) + np.cos(2*np.pi*y))

# SA solver
def simulated_annealing(T0=5.0, T_min=0.001, alpha=0.995, steps=5000):
    x, y = np.random.uniform(-4, 4), np.random.uniform(-4, 4)
    E = rastrigin(x, y)
    T = T0
    history = [(x, y, E)]
    for _ in range(steps):
        xn = x + np.random.normal(0, 0.3)
        yn = y + np.random.normal(0, 0.3)
        En = rastrigin(xn, yn)
        dE = En - E
        if dE < 0 or np.random.rand() < np.exp(-dE / T):
            x, y, E = xn, yn, En
        history.append((x, y, E))
        T = max(T * alpha, T_min)
    return np.array(history)

np.random.seed(13)
paths = [simulated_annealing() for _ in range(4)]

# Background landscape
xx, yy = np.meshgrid(np.linspace(-4, 4, 200), np.linspace(-4, 4, 200))
Z = rastrigin(xx, yy)

fig, axes = plt.subplots(1, 2, figsize=(15, 6))
fig.patch.set_facecolor('#030712')

# Left: trajectory over landscape
ax1 = axes[0]
ax1.set_facecolor('#1a0a2e')
cs = ax1.contourf(xx, yy, Z, 30, cmap='magma', alpha=0.85)
colors = ['#e879f9', '#22d3ee', '#fbbf24', '#86efac']
for p, c in zip(paths, colors):
    ax1.plot(p[:, 0], p[:, 1], color=c, linewidth=1.0, alpha=0.75)
    ax1.scatter(p[0, 0], p[0, 1], c=c, s=90, marker='^', edgecolors='white', linewidth=1, zorder=5)
    ax1.scatter(p[-1, 0], p[-1, 1], c=c, s=120, marker='*', edgecolors='white', linewidth=1, zorder=5)
ax1.scatter(0, 0, c='white', s=200, marker='x', linewidth=3, zorder=6, label='Global min')
ax1.set_xlabel('x', color='white'); ax1.set_ylabel('y', color='white')
ax1.set_title('SA Trajectories on Rastrigin Landscape', color='#f0abfc')
ax1.tick_params(colors='white'); ax1.legend(facecolor='#1a0a2e', edgecolor='#c084fc', labelcolor='white')
for sp in ax1.spines.values(): sp.set_color('#c084fc')

# Right: energy history
ax2 = axes[1]
ax2.set_facecolor('#1a0a2e')
for p, c in zip(paths, colors):
    ax2.plot(p[:, 2], color=c, linewidth=1.2, alpha=0.85)
ax2.set_xlabel('Step', color='white'); ax2.set_ylabel('Energy (Rastrigin)', color='white')
ax2.set_title('Energy convergence (4 independent runs)', color='#f0abfc')
ax2.tick_params(colors='white'); ax2.grid(True, alpha=0.25, color='#a78bfa')
for sp in ax2.spines.values(): sp.set_color('#c084fc')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#030712')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

0.6 The Biomimicry Design Spiral

Biomimicry 3.8 (the consultancy founded by Benyus) formalised a step-wise method called the Biomimicry Design Spiral for systematically using biology in the design process:

Identify — define the function to be performed.
Translate — rephrase in biological terms: “How does nature...?”
Discover — search the biological literature (AskNature database) for champions.
Abstract — distil design principles from the biology.
Emulate — prototype with engineering materials / processes.
Evaluate — test against Life's Principles and conventional benchmarks.

The AskNature database (asknature.org) is a curated, function-indexed catalogue of thousands of biological strategies, maintained by the Biomimicry Institute. Subsequent modules use it repeatedly.

0.5a Fitness Landscapes and the Price Equation

Sewall Wright (1932) introduced the fitness landscape: a surface in genotype space where altitude corresponds to reproductive fitness. Evolution proceeds as hill-climbing on this landscape, biased by drift and mutation. The engineering problem of biomimetics is equivalent to asking: what peaks has nature already discovered, and can we descend from them to neighbouring peaks for our own applications?

\( \Delta \bar{w} = \text{Cov}(w, z) + E[w \Delta z] \)

The Price equation (Price 1970) decomposes change in mean fitness \(\bar w\) into a covariance term (selection) and an expectation term (transmission). It is the fundamental theorem of natural selection, applicable equally to biological evolution and to genetic algorithms.

The dimensionality of biological fitness landscapes is enormous: a protein of length 100 residues has \(20^{100} \approx 10^{130}\) possible sequences. Yet nature has navigated this space to specific solutions (e.g. the cytochrome c fold is conserved across all aerobic life). This is either because the landscape is smooth (“holey” Gavrilets 1997) or because most sequences are equivalent under neutral drift. Either view implies that small search algorithms (GAs with 10²–10⁴ individuals) can find useful solutions.

0.5b Allometric Scaling: Why Copying Biology Requires Careful Scaling

A recurring pitfall is naive linear scaling of biological solutions. The Reynolds number\( \text{Re} = \rho v L / \mu \) is a classic example: a biomimetic MAV based on hummingbird flight operates at \(\text{Re} \sim 10^4\), where viscous forces dominate and leading-edge vortices behave entirely differently from the \(\text{Re} \sim 10^6\)regime of a Boeing 747.

\( \text{Re} = \frac{\rho v L}{\mu} \)

Similarly, the surface-to-volume ratio scales as \(L^{-1}\); a gecko that is 10x larger than a typical one cannot cling, because its body mass scales as \(L^3\) while its adhesive area scales as \(L^2\). A 100 kg gecko-robot is physically impossible with planar setae and van der Waals contact alone — it requires claws or suction augmentation.

Kleiber's law \( B \propto M^{3/4} \) (basal metabolic rate vs body mass) illustrates how fundamental biological constraints depend on size. Biomimetic designs must identify which scaling regime the biological source operates in and engineer accordingly.

0.7 Cross-Links to Other Courses

Biomimetics sits at the intersection of biology, physics, chemistry, and engineering. Throughout this course we will reference:

• Spider Biophysics — silk nanostructure, web mechanics, hydraulic locomotion.
• Bee Biophysics — honeycomb geometry, waggle-dance navigation, flapping flight.
• Insect Biophysics — compound eyes, clap-and-fling, exoskeletal mechanics.
• Plant Biochemistry — photosynthesis, phototropism, lotus effect source.
• Avian Biophysics — feathers, wing morphology, silent flight.
• Biophysics — molecular motors, ion channels, cellular mechanics.

0.7a Landmark Biomimetic Technologies

Eight flagship case studies that recur throughout this course. Each will be examined in depth in the relevant module; here we record the canonical reference and the key engineering figure of merit.

Technology	Biological source	Key figure of merit	Module
Velcro hook-and-loop	Burdock burrs	5 N/cm² reversible adhesion	M0, M2
Speedo Fastskin LZR Racer	Shark skin denticles	5 - 10% drag reduction	M2
Lotusan paint (Sto AG)	Lotus leaf micro-bumps	Contact angle theta > 150 deg	M2
Eastgate Centre, Harare	Termite mound ventilation	90% less HVAC energy	M6
Shinkansen 500 bullet train	Kingfisher beak	Eliminated tunnel sonic boom	M3
Stickybot (Stanford)	Gecko setae	Climbs dry vertical glass	M2
WhalePower blades	Humpback pectoral fins	20% better low-speed lift	M3
Festo SmartBird	Herring gull flight	L/D = 14 in flapping flight	M3

0.8 Summary & References

• Biomimicry has deep historical roots (da Vinci) but became a formal discipline with Benyus (1997).
• Six “Life's Principles” provide diagnostic and prescriptive criteria.
• Three levels (form / process / ecosystem) increase in depth and impact.
• Performance index \(\eta = P_{\text{bio}}/P_{\text{conv}}\) quantifies gain; Ashby charts multi-criterion.
• Evolution is a massively parallel optimization algorithm formalised as GA / SA.
• The Biomimicry Design Spiral operationalises the discipline in six steps.

References

[1] Benyus, J.M. (1997). Biomimicry: Innovation Inspired by Nature. Harper Perennial.
[2] Vincent, J.F.V. et al. (2006). Biomimetics — its practice and theory. J. R. Soc. Interface 3, 471–482.
[3] Pedersen Zari, M. (2007). Biomimetic approaches to architectural design for increased sustainability. SB07 NZ Conference.
[4] Holland, J.H. (1975). Adaptation in Natural and Artificial Systems. Univ. Michigan Press.
[5] Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P. (1983). Optimization by simulated annealing. Science 220, 671–680.
[6] Ashby, M.F. (2011). Materials Selection in Mechanical Design, 4th ed. Butterworth-Heinemann.
[7] Bhushan, B. (2016). Biomimetics: Bioinspired Hierarchical-Structured Surfaces, 2nd ed. Springer.
[8] McDonough, W., Braungart, M. (2002). Cradle to Cradle: Remaking the Way We Make Things. North Point Press.
[9] Koza, J.R. (1992). Genetic Programming. MIT Press.
[10] AskNature (Biomimicry Institute). asknature.org.

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