绘制尖峰突变表面(带有gnuplot) [英] plot surface of cusp catastrophe (with gnuplot)

问题描述

是否可以使用Gnuplot绘制 Cusp Catastrophe 的表面?这是一个可比图.

• 巨灾的数学描述为:V = x ^ 4 + a * x ^ 2 + b * x(维基百科，见上文)
• 表面描述为:0 = a + b * y – y ^ 3

我是gnu情节的初学者，因此，我非常感谢您提供源代码示例.

(我研究心理学并且需要这张图来撰写有关临床理论的文章:尖峰灾难用于描述情绪变化，与健康人相比，抑郁症患者的情绪变化似乎更为突然和破坏性.) /p>

解决方案

我认为最好的方法是生成方程式的根表(在gnuplot之外)，然后用散点图绘制该表.但是您可以通过尝试在gnuplot中获得所需的近似值

a=b=1
set para
set iso 30
set pm3d at s
set urange [-10:10]
set hidd
set view 47,192
splot a + u*v - b * v**3, u, v

Is it possible to plot the surface of the Cusp Catastrophe with Gnuplot? Here's a comparable plot.

• The catastrophe is mathematically described by: V = x^4 + a*x^2 + b*x (Wikipedia, see above)
• The surface is describes by: 0 = a + b*y – y^3

I'm a gnu plot beginner, so I'd be really grateful for an example with source code.

(I study psychology and I need this plot for an essay about a clinical theory: the cusp catastrophe is used to describe changes of mood, that seem to appear more sudden and disruptive for depressive patients, compared to healthy persons.)

解决方案

I think the best way would be to generate a table of roots of the equation (outside of gnuplot) and then plot the table with splot. But you can get an approximation to what you want in gnuplot by trying

a=b=1
set para
set iso 30
set pm3d at s
set urange [-10:10]
set hidd
set view 47,192
splot a + u*v - b * v**3, u, v

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