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Module 1: Locomotion & Biomechanics

Ant locomotion encompasses one of the broadest performance envelopes in the animal kingdom. From the steady marching of army ants to the explosive mandible strikes of trap-jaw ants (accelerations exceeding $10^5 \, g$), from vibration-enhanced leaf cutting to cooperative transport of objects 100x any individual's capacity, the biomechanics of ants reveal fundamental principles of legged locomotion, elastic energy storage, and collective mechanics.

1. Alternating Tripod Gait

The fundamental gait of most ants is the alternating tripod gait, in which the six legs move in two groups of three. Tripod A consists of the left foreleg (L1), right middle leg (R2), and left hind leg (L3); Tripod B consists of R1, L2, and R3. While one tripod is in stance phase (pushing against the ground), the other is in swing phase (moving forward through the air).

1.1 Static Stability

The tripod gait provides static stability: at every instant during locomotion, the center of mass (CoM) lies within the triangle of support formed by the three legs in stance phase. The stability margin is defined as the minimum distance from the CoM projection to the nearest edge of the support polygon:

\[ S_m = \min_i \left( d(\mathbf{r}_{\text{CoM}}, \text{edge}_i) \right) \]

where $d$ is the perpendicular distance from CoM to edge $i$ of the support triangle

Static stability requires $S_m > 0$ at all times. For typical ant body proportions, the stability margin during tripod gait is approximately:

\[ S_m \approx \frac{w}{2} - \frac{l_{\text{body}}}{2} \cdot \sin\alpha \]

where $w$ is the leg span, $l_{\text{body}}$ is body length, and $\alpha$ is the body yaw angle

1.2 Duty Factor

The duty factor $\beta$ is the fraction of each stride cycle that a leg spends in stance phase:

\[ \beta = \frac{t_{\text{stance}}}{t_{\text{stance}} + t_{\text{swing}}} = \frac{t_{\text{stance}}}{T_{\text{stride}}} \]

For static stability with a tripod gait, $\beta > 0.5$ is required (each tripod must be on the ground for more than half the cycle). At slow speeds, ants typically have $\beta \approx 0.6\text{--}0.7$. As speed increases,$\beta$ decreases toward 0.5 and eventually below 0.5 at the highest speeds, transitioning to a dynamically stable regime with aerial phases.

1.3 Froude Number and Gait Transitions

The Froude number for legged locomotion is defined as:

\[ \text{Fr} = \frac{v^2}{g \ell} \]

where $v$ is forward speed, $g$ is gravitational acceleration, and $\ell$ is effective leg length

In vertebrates, the walk-to-run transition occurs near $\text{Fr} \approx 0.5\text{--}1$. Many ants, however, operate at remarkably high Froude numbers. The Saharan silver ant (Cataglyphis bombycina) achieves speeds of up to$v = 0.855 \;\text{m/s}$ with leg length $\ell \approx 1.5 \;\text{mm}$:

\[ \text{Fr} = \frac{(0.855)^2}{9.81 \times 0.0015} \approx 50 \]

This is an extraordinary Froude number — far higher than the $\text{Fr} \approx 2.5$ of a galloping horse. At these speeds, Cataglyphis exhibits an aerial phase where all six legs are simultaneously off the ground, effectively "galloping" with a stride frequency of $\sim 40 \;\text{Hz}$ and leg contact times below$7 \;\text{ms}$ per step.

1.4 Speed Scaling

Maximum running speed across ant species scales allometrically with body mass:

\[ v_{\max} \propto M^{0.17\text{--}0.25} \]

However, relative speed (in body lengths per second) scales inversely with size. Cataglyphis bombycina, at only$\sim 6 \;\text{mg}$, achieves roughly 100 body lengths per second —making it one of the fastest animals on Earth relative to body size. For comparison, a cheetah at top speed covers about 16 body lengths per second.

2. Trap-Jaw Mechanics

The trap-jaw ant genus Odontomachus possesses the fastest self-powered predatory appendage in the animal kingdom. The mandible strike closes in approximately $0.13 \;\text{ms}$, reaching tip velocities of$64 \;\text{m/s}$ with peak accelerations of$10^5 \times g \approx 10^6 \;\text{m/s}^2$.

2.1 Latch-Mediated Spring Actuation (LMSA)

These extreme kinematics are impossible through direct muscle contraction. Instead, trap-jaw ants use a latch-mediated spring actuation (LMSA) mechanism:

Loading phase ($\sim 500 \;\text{ms}$): Large closer muscles contract slowly, storing elastic energy in deformable regions of the head capsule (resilin-rich cuticle acts as a spring).
Latched state: A trigger hair (sensory seta) on the inner surface of the mandible acts as the sensory trigger. The mandible is held open by a mechanical latch — a specialized cuticular process.
Release phase ($\sim 0.13 \;\text{ms}$): When prey contacts the trigger hair, the latch releases and stored elastic energy is converted to kinetic energy in the mandible.

2.2 Energy and Power Analysis

The kinetic energy of the mandible at closure is:

\[ E_k = \frac{1}{2} I \omega^2 = \frac{1}{2} m_{\text{mand}} v^2 \]

For Odontomachus bauri:

$\bullet$ Mandible mass: $m_{\text{mand}} \approx 1.5 \times 10^{-7} \;\text{kg}$ (0.15 mg)
$\bullet$ Tip velocity: $v = 64 \;\text{m/s}$
$\bullet$ Closure time: $\Delta t = 1.3 \times 10^{-4} \;\text{s}$

\[ E_k = \frac{1}{2} \times 1.5 \times 10^{-7} \times (64)^2 \approx 3.1 \times 10^{-4} \;\text{J} = 0.31 \;\text{mJ} \]

The velocity of the mandible tip can be related to the stored elastic energy by conservation of energy (assuming the latch mechanism is efficient):

\[ v = \sqrt{\frac{2 E_{\text{stored}}}{m_{\text{mand}}}} \]

2.3 Power Amplification

The key insight is the power amplification. Muscle-specific power output is limited to about $100\text{--}300 \;\text{W/kg}$across all animals. The peak instantaneous power during the mandible strike is:

\[ P_{\text{strike}} = \frac{E_k}{\Delta t} = \frac{3.1 \times 10^{-4}}{1.3 \times 10^{-4}} \approx 2.4 \;\text{W} \]

The closer muscle mass is approximately $m_{\text{muscle}} \approx 2 \;\text{mg}$. The mass-specific strike power is:

\[ \frac{P_{\text{strike}}}{m_{\text{muscle}}} = \frac{2.4}{2 \times 10^{-6}} = 1.2 \times 10^6 \;\text{W/kg} \]

This is roughly 10,000 times the maximum muscle power output, confirming that the energy must be stored elastically and released through a power amplification mechanism. The muscles cannot produce this power directly — they are too slow.

2.4 Escape Jumping

Remarkably, Odontomachus also uses its mandible strike for escape jumping. By striking the mandibles against the ground, the ant launches itself into the air. The mandible-ground impact generates forces of 300–500 times body weight, propelling the ant to heights of 8–10 cm (approximately 40 body lengths). The takeoff dynamics follow:

\[ h_{\max} = \frac{v_{\text{takeoff}}^2}{2g} = \frac{v_{\text{mandible}}^2 \cdot m_{\text{mand}}}{2 g \cdot m_{\text{body}}} \]

(momentum transfer from mandible to body via ground reaction force)

3. Leaf-Cutter Jaw Mechanics

Leaf-cutter ants (Atta and Acromyrmex) are the dominant herbivores of the Neotropics, harvesting more plant biomass per hectare than any other animal group. Their leaf-cutting ability relies on a sophisticated combination of sharp mandible geometry, vibration-enhanced cutting, and zinc-hardened cutting edges.

3.1 Vibration-Enhanced Cutting

While cutting, leaf-cutter ants vibrate their mandibles at high frequency ($\sim 1 \;\text{kHz}$) using a stridulatory organ located on the gaster. The stridulitrum consists of a file (pars stridens) on the 3rd abdominal tergite and a scraper (plectrum) on the 4th. Vibration is transmitted through the body to the mandibles.

The vibration reduces the effective cutting force by a mechanism analogous to ultrasonic cutting in engineering. For a vibrating blade with amplitude $A$ and angular frequency $\omega$, the cutting force reduction relative to static cutting is:

\[ F_{\text{cut}}^{\text{vib}} = F_{\text{cut}}^{\text{static}} \cdot \left(1 - \frac{A \omega^2}{F_N / m}\right) \]

where $F_N$ is the normal force applied and $m$ is the effective vibrating mass

Experimental measurements by Tautz et al. (1995) showed that vibration reduces the force required for leaf cutting by approximately 30–50%, significantly reducing energetic cost and mandible wear.

3.2 Fracture Mechanics of Leaf Cutting

The mandible cuts through the leaf by propagating a crack. The energy release rate for crack propagation in a leaf lamina is:

\[ G = \frac{K_I^2}{E_{\text{leaf}}} + \frac{K_{II}^2}{E_{\text{leaf}}} \]

combined Mode I (opening) and Mode II (shearing) fracture

The mandible geometry is optimized for this cutting mode. The blade edge is curved (not straight), with a radius of curvature that maintains approximately constant stress intensity factor along the cut line. The tip radius of the cutting edge is $\sim 50 \;\text{nm}$ —sharper than a surgical scalpel ($\sim 300 \;\text{nm}$).

3.3 Mandible Tooth Geometry

The mandible bears a series of teeth along its inner margin. In Atta cephalotes, there are typically 8–12 teeth with specific spacing related to the thickness of leaf tissue. The tooth spacing $\lambda_t$ is optimized relative to the leaf thickness $t_{\text{leaf}}$:

\[ \lambda_t \approx 2\text{--}3 \times t_{\text{leaf}} \]

This ensures that each tooth engages with the leaf independently, preventing the blade from clogging and maintaining efficient cutting. The mandible operates as a serrated blade where each tooth concentrates stress at discrete points along the cut line, lowering the total force required.

3.4 Age-Related Mandible Wear

Despite zinc-enrichment, mandibles do wear over time. Older workers with dull mandibles are reassigned from cutting to carrying tasks — an elegant example of task allocation optimized by physical constraints. The cutting efficiency declines as:

\[ \eta_{\text{cut}}(t) = \eta_0 \cdot e^{-t/\tau_{\text{wear}}} \]

where $\tau_{\text{wear}} \approx 30\text{--}60 \;\text{days}$ depending on leaf toughness

4. Load Carriage & Cooperative Transport

Ants carry loads using two primary strategies: overhead carriage(holding the load above the body with mandibles, typical of leaf-cutter ants) and dragging (pulling the load along the ground). The biomechanics differ substantially.

4.1 Overhead Carriage Biomechanics

When an ant carries a leaf fragment overhead, the load shifts the center of mass upward and backward. The ant compensates by:

Tilting the body forward (pitching the mesosoma)
Adjusting leg kinematics (wider stance, shorter stride)
Reducing speed by $\sim 50\%$ compared to unladen locomotion

The torque balance about the center of the mesosoma requires:

\[ m_{\text{load}} g \cdot d_{\text{load}} = F_{\text{legs}} \cdot d_{\text{legs}} \]

where $d_{\text{load}}$ is the horizontal distance from CoM to load, and $d_{\text{legs}}$ is the moment arm of compensatory leg forces

4.2 Cooperative Transport

When an item is too large for a single ant, multiple ants engage in cooperative transport. This is one of the most remarkable collective behaviors in ants, because the group can transport objects 100–1000x any individual's carrying capacity without explicit coordination or communication about direction.

The physics of cooperative transport follows from vector addition of individual forces. If$N$ ants each exert force $\mathbf{F}_i$ on the load, the net force is:

\[ \mathbf{F}_{\text{net}} = \sum_{i=1}^{N} \mathbf{F}_i \]

If forces are randomly directed, $|\mathbf{F}_{\text{net}}| \propto \sqrt{N}$(random walk in force space). But ants achieve near-linear scaling ($|\mathbf{F}_{\text{net}}| \propto N$) through a simple rule: each ant pulls toward the nest, and informed ants (who know where the nest is) can steer the group. The alignment mechanism involves:

Individual ants align their pulling direction based on proprioceptive feedback from the load's motion
Ants arriving at the load pull in their individual nest-ward direction
The load's slow rotation provides a mechanical feedback that gradually aligns all participants

The effective friction coefficient for a dragged load is:

\[ F_{\text{drag}} = \mu_k \cdot m_{\text{load}} \cdot g \]

with $\mu_k \approx 0.3\text{--}0.8$ depending on substrate

The minimum number of ants required for cooperative transport is thus:

\[ N_{\min} = \frac{\mu_k \cdot m_{\text{load}} \cdot g}{F_{\text{individual}} \cdot \cos\bar{\theta}} \]

where $\bar{\theta}$ is the mean angular deviation from the transport direction

5. Tripod Gait Pattern & Stability

The diagram below shows a dorsal (top-down) view of the ant during one half-cycle of the tripod gait. Understanding this requires three key ideas:

1. Two Tripods Alternate

The 6 legs split into two groups of 3. Tripod A (L1, R2, L3 — red filled circles) is on the ground providing support, while Tripod B (R1, L2, R3 — blue open circles) swings forward through the air. Then they switch.

2. Support Triangle

The three stance legs form a triangle (dashed red). As long as the center of mass (yellow dot, CoM) stays inside this triangle, the ant is statically stable — it won't topple. The distance from CoM to the nearest triangle edge is the stability margin.

3. Ground Reaction Forces

Each stance leg pushes against the ground (cyan GRF arrows). The vector sum of all three GRFs must equal the ant's weight plus any acceleration forces. At high speed, the duty factor $\beta$ drops to ~0.5 (each leg spends equal time in stance and swing).

6. Locomotion Simulation

The simulation below visualizes four key aspects of ant locomotion: (1) the alternating tripod gait timing diagram showing stance and swing phases, (2) elastic energy storage and explosive release in the trap-jaw mechanism, (3) maximum running speed across ant species, and (4) Froude number regimes and gait transitions.

Python

script.py203 lines

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

fig, axes = plt.subplots(2, 2, figsize=(16, 14))
fig.patch.set_facecolor('#030712')
fig.suptitle("Ant Locomotion & Biomechanics", fontsize=16, color='white', fontweight='bold', y=0.98)

# ── Panel 1: Tripod Gait Timing Diagram ──
ax1 = axes[0, 0]
ax1.set_facecolor('#1a0505')

legs = ['L1', 'R2', 'L3', 'R1', 'L2', 'R3']
leg_labels = ['Left fore (L1)', 'Right mid (R2)', 'Left hind (L3)',
              'Right fore (R1)', 'Left mid (L2)', 'Right hind (R3)']
# Tripod A: L1, R2, L3 - swing first
# Tripod B: R1, L2, R3 - swing when A is in stance
duty_factor = 0.6  # fraction of cycle in stance
n_cycles = 3
cycle_period = 1.0

for i, leg in enumerate(legs):
    y_pos = i
    is_tripod_a = i < 3
    for c in range(n_cycles):
        t_start = c * cycle_period
        if is_tripod_a:
            # swing phase first
            swing_start = t_start
            swing_end = t_start + (1 - duty_factor) * cycle_period
            stance_start = swing_end
            stance_end = t_start + cycle_period
        else:
            # stance phase first (offset by half cycle)
            stance_start = t_start
            stance_end = t_start + duty_factor * cycle_period
            swing_start = stance_end
            swing_end = t_start + cycle_period

# Draw stance (solid) and swing (hollow)
        ax1.barh(y_pos, stance_end - stance_start, left=stance_start, height=0.6,
                color='#f87171', edgecolor='#fca5a5', linewidth=0.5, alpha=0.8)
        ax1.barh(y_pos, swing_end - swing_start, left=swing_start, height=0.6,
                color='#1a0505', edgecolor='#f87171', linewidth=1, alpha=0.8)

ax1.set_yticks(range(6))
ax1.set_yticklabels(leg_labels, fontsize=9, color='white')
ax1.set_xlabel('Time (stride periods)', color='white', fontsize=11)
ax1.set_title('Alternating Tripod Gait Pattern\nSolid = stance, Hollow = swing', color='#fca5a5', fontsize=12)
ax1.tick_params(colors='white')
ax1.set_xlim(0, 3)
# Add tripod group labels
ax1.text(-0.15, 1, 'Tripod A', transform=ax1.get_yaxis_transform(),
         fontsize=10, color='#f87171', fontweight='bold', rotation=90, va='center')
ax1.text(-0.15, 4, 'Tripod B', transform=ax1.get_yaxis_transform(),
         fontsize=10, color='#fbbf24', fontweight='bold', rotation=90, va='center')
ax1.axhline(y=2.5, color='#94a3b8', linewidth=1, linestyle='--', alpha=0.5)
for sp in ax1.spines.values():
    sp.set_color('#f87171')
ax1.grid(True, alpha=0.1, color='#f87171', axis='x')

# ── Panel 2: Trap-Jaw Energy Storage & Release ──
ax2 = axes[0, 1]
ax2.set_facecolor('#1a0505')

# Latch-mediated spring actuation model
# Muscle loads spring over ~500ms, spring releases in ~0.13ms
t_load = np.linspace(0, 500, 500)  # ms
t_release = np.linspace(500, 500.13, 200)  # ms
t_after = np.linspace(500.13, 510, 100)

# Energy stored (muscle loading)
E_max = 5e-6  # 5 microjoules
E_load = E_max * (1 - np.exp(-t_load / 100))
E_release = E_max * np.exp(-(t_release - 500) / 0.02)
E_after = np.zeros_like(t_after)

t_all = np.concatenate([t_load, t_release, t_after])
E_all = np.concatenate([E_load, E_release, E_after])

ax2.plot(t_all, E_all * 1e6, color='#f87171', linewidth=2.5)
ax2.fill_between(t_all, E_all * 1e6, alpha=0.2, color='#f87171')

# Add phases
ax2.axvspan(0, 500, alpha=0.05, color='#fbbf24')
ax2.axvspan(500, 500.13, alpha=0.15, color='#ef4444')
ax2.text(250, 4.5, 'Muscle loading\n(~500 ms)', color='#fbbf24', fontsize=10,
         ha='center', fontweight='bold')
ax2.text(505, 3, 'Release!\n(0.13 ms)', color='#ef4444', fontsize=10, fontweight='bold')

# Power annotation
ax2.annotate(f'P_muscle ~ 100 W/kg\nP_strike ~ 10$^6$ W/kg\n(10,000x amplification)',
             xy=(505, 2), fontsize=9, color='#fca5a5',
             bbox=dict(boxstyle='round', facecolor='#1a0505', edgecolor='#f87171'))

ax2.set_xlabel('Time (ms)', color='white', fontsize=11)
ax2.set_ylabel('Stored Elastic Energy (uJ)', color='white', fontsize=11)
ax2.set_title('Trap-Jaw: Latch-Mediated Spring Actuation\nOdontomachus bauri', color='#fca5a5', fontsize=12)
ax2.tick_params(colors='white')
for sp in ax2.spines.values():
    sp.set_color('#f87171')
ax2.grid(True, alpha=0.15, color='#f87171')

# ── Panel 3: Speed vs Body Mass ──
ax3 = axes[1, 0]
ax3.set_facecolor('#1a0505')

ants = [
    ("Cataglyphis bombycina", 6e-6, 0.855, '#ef4444'),
    ("Cataglyphis fortis", 1e-5, 0.6, '#f87171'),
    ("Ocymyrmex", 8e-6, 0.5, '#fb923c'),
    ("Formica rufa", 8e-6, 0.3, '#f87171'),
    ("Iridomyrmex", 1.5e-6, 0.15, '#f87171'),
    ("Pheidole", 5e-7, 0.03, '#fca5a5'),
    ("Atta cephalotes", 2e-6, 0.02, '#dc2626'),
    ("Paraponera clavata", 3e-5, 0.03, '#b91c1c'),
    ("Eciton burchellii", 5e-6, 0.035, '#f87171'),
    ("Solenopsis invicta", 1.5e-6, 0.04, '#ef4444'),
    ("Camponotus", 1e-5, 0.05, '#f87171'),
    ("Dorylus", 2e-5, 0.04, '#dc2626'),
]

for name, mass, speed, color in ants:
    ax3.scatter(mass * 1e3, speed, c=color, s=90, edgecolors='white', linewidth=0.5, zorder=5)
    ax3.annotate(name, (mass * 1e3, speed), fontsize=7, color='white',
                 xytext=(5, 3), textcoords='offset points', fontstyle='italic')

# Highlight fastest
ax3.annotate('Fastest ant!\n~100 body lengths/s',
             xy=(6e-3, 0.855), xytext=(0.02, 0.7),
             arrowprops=dict(arrowstyle='->', color='#fbbf24', linewidth=1.5),
             fontsize=9, color='#fbbf24', fontweight='bold')

# Allometric fit
m_arr = np.array([a[1] for a in ants]) * 1e3
v_arr = np.array([a[2] for a in ants])
log_m = np.log10(m_arr)
log_v = np.log10(v_arr)
slope, intercept = np.polyfit(log_m, log_v, 1)
m_fit = np.logspace(-4, -1, 100)
v_fit = 10**intercept * m_fit**slope
ax3.plot(m_fit, v_fit, color='#fbbf24', linewidth=2, linestyle='--', alpha=0.6,
         label=f'v ~ M$^{{{slope:.2f}}}$')

ax3.set_xscale('log')
ax3.set_yscale('log')
ax3.set_xlabel('Body Mass (mg)', color='white', fontsize=11)
ax3.set_ylabel('Maximum Speed (m/s)', color='white', fontsize=11)
ax3.set_title('Running Speed vs Body Mass\nAcross Ant Species', color='#fca5a5', fontsize=12)
ax3.tick_params(colors='white')
for sp in ax3.spines.values():
    sp.set_color('#f87171')
ax3.grid(True, alpha=0.15, color='#f87171')
ax3.legend(fontsize=9, facecolor='#1a0505', edgecolor='#f87171', labelcolor='white')

# ── Panel 4: Froude Number & Gait Transitions ──
ax4 = axes[1, 1]
ax4.set_facecolor('#1a0505')

# Froude number = v^2 / (g * L_leg)
leg_lengths = np.linspace(0.5e-3, 5e-3, 200)
g = 9.81

speeds_slow = np.sqrt(0.5 * g * leg_lengths)  # Fr = 0.5
speeds_trans = np.sqrt(1.0 * g * leg_lengths)  # Fr = 1.0
speeds_fast = np.sqrt(2.0 * g * leg_lengths)   # Fr = 2.0
speeds_aerial = np.sqrt(5.0 * g * leg_lengths) # Fr = 5.0

ax4.fill_between(leg_lengths * 1e3, speeds_slow * 1e3, 0,
                 alpha=0.15, color='#22d3ee', label='Fr < 0.5 (walking)')
ax4.fill_between(leg_lengths * 1e3, speeds_trans * 1e3, speeds_slow * 1e3,
                 alpha=0.15, color='#fbbf24', label='0.5 < Fr < 1 (transition)')
ax4.fill_between(leg_lengths * 1e3, speeds_aerial * 1e3, speeds_trans * 1e3,
                 alpha=0.15, color='#f87171', label='Fr > 1 (aerial phase)')

ax4.plot(leg_lengths * 1e3, speeds_slow * 1e3, '#22d3ee', linewidth=1.5)
ax4.plot(leg_lengths * 1e3, speeds_trans * 1e3, '#fbbf24', linewidth=2)
ax4.plot(leg_lengths * 1e3, speeds_fast * 1e3, '#f87171', linewidth=1.5)
ax4.plot(leg_lengths * 1e3, speeds_aerial * 1e3, '#ef4444', linewidth=1.5, linestyle='--')

# Mark some ant species
ax4.scatter([1.5], [120], c='#f87171', s=100, edgecolors='white', linewidth=1, zorder=5, marker='*')
ax4.annotate('Cataglyphis\n(Fr ~ 20!)', xy=(1.5, 120), xytext=(2.5, 150),
             arrowprops=dict(arrowstyle='->', color='white'), fontsize=9, color='#fca5a5')

ax4.scatter([1.0], [30], c='#fb923c', s=80, edgecolors='white', linewidth=1, zorder=5)
ax4.annotate('Formica', xy=(1.0, 30), xytext=(2.0, 50),
             arrowprops=dict(arrowstyle='->', color='white'), fontsize=9, color='#fca5a5')

ax4.set_xlabel('Leg Length (mm)', color='white', fontsize=11)
ax4.set_ylabel('Speed (mm/s)', color='white', fontsize=11)
ax4.set_title('Froude Number Gait Regimes\nFr = v$^2$/(gL)', color='#fca5a5', fontsize=12)
ax4.tick_params(colors='white')
for sp in ax4.spines.values():
    sp.set_color('#f87171')
ax4.grid(True, alpha=0.15, color='#f87171')
ax4.legend(fontsize=8, facecolor='#1a0505', edgecolor='#f87171', labelcolor='white', loc='upper left')

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

References

1. Full, R. J., & Tu, M. S. (1991). Mechanics of a rapid running insect: two-, four- and six-legged locomotion. Journal of Experimental Biology, 156(1), 215–231.

2. Patek, S. N., Baio, J. E., Fisher, B. L., & Suarez, A. V. (2006). Multifunctionality and mechanical origins: ballistic jaw propulsion in trap-jaw ants. Proceedings of the National Academy of Sciences, 103(34), 12787–12792.

3. Tautz, J., Roces, F., & Hölldobler, B. (1995). Use of a sound-based vibratome by leaf-cutting ants. Science, 267(5194), 84–87.

4. Pfeffer, S. E., Wittlinger, M., & Wolf, H. (2019). Cataglyphis desert ants: high-speed locomotion in thermally extreme environments. Journal of Comparative Physiology A, 205, 725–740.

5. Reinhardt, L., & Blickhan, R. (2014). Level locomotion in wood ants: evidence for grounded running. Journal of Experimental Biology, 217(13), 2358–2370.

6. Lipp, A., Wolf, H., & Lehmann, F. O. (2005). Walking on inclines: energetics of locomotion in the ant Camponotus. Journal of Experimental Biology, 208(4), 707–719.

7. McCreery, H. F., & Bhatt, B. (2020). Cooperative transport in ants: review of proximate mechanisms. Insectes Sociaux, 67, 29–45.

8. Schofield, R. M. S. (2001). Metals in cuticular structures. In Scorpions 2001. In Memoriam Gary A. Polis (pp. 234–245).

9. Zollikofer, C. P. (1994). Stepping patterns in ants — influence of speed and curvature. Journal of Experimental Biology, 192(1), 95–106.

10. Gravish, N., et al. (2013). Effects of worker size on the dynamics of fire ant tunnel construction. Journal of the Royal Society Interface, 9(77), 3312–3322.

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