Generate bifurcation diagrams for dynamical systems. Use when visualizing parameter-dependent behavior transitions.
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Generates bifurcation diagrams showing how system behavior changes with parameters.
PLUS (+1) Generator - creates visual outputs from system parameters.
# Logistic map bifurcation
import numpy as np
import matplotlib.pyplot as plt
def logistic_bifurcation(r_min=2.5, r_max=4.0, steps=1000):
r_vals = np.linspace(r_min, r_max, steps)
x = 0.5
for r in r_vals:
for _ in range(100): # transient
x = r * x * (1 - x)
for _ in range(50): # attractor
x = r * x * (1 - x)
yield r, x
This skill (PLUS +1) pairs with bifurcation (ERGODIC 0) for balanced analysis:
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Model ElevenLabs voice synthesis as an ACSet schema with Unison ability handlers for typed voice operations. Use when integrating ElevenLabs TTS into category-theoretic pipelines, building typed voice synthesis workflows, or managing multi-voice narration with GF(3) conservation.
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Systematic process for analyzing and modernizing legacy applications to comply with the 12-Factor App methodology. Covers code analysis, configuration externalization, dependency management, and container/Kubernetes best practices.
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Gay MCP skill at invocation 26
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Gay MCP skill at invocation 3
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