Prompt: The parameters of a dynamic equation evolve as the equation is iterated, and the specific values may depend on the starting parameters. An example is the well-studied logistic map, x n + 1 = r x n ( 1 − x n ) {\displaystyle x_{n+1}=rx_{n}(1-x_{n})}, whose basins of attraction for various values of the parameter r r are shown in the figure. If r = 2.6 {\displaystyle r=2.6}, all starting x x values of x < 0 x<0 will rapidly lead to function values that go to negative infinity; starting x x values of x > 1 x>1 will also go to negative infinity. But for 0 < x < 1 0<x<1 the x x values rapidly converge to x ≈ 0.615 {\displaystyle x\approx 0.615}, i.e. at this value of r r, a single value of x x is an attractor for the function's behaviour. For other values of r r, more than one value of x x may be visited: if r r is 3.2, starting values of 0 < x < 1 0<x<1 will lead to function values that alternate between x ≈ 0.513 {\displaystyle x\approx 0.513} and x ≈ 0.799 {\displaystyle x\approx 0.799}. At some values of r r, the attractor is a single point (a "fixed point"), at other values of r r two values of x x are visited in turn (a period-doubling bifurcation), or, as a result of furt
Prompt: The parameters of a dynamic equation evolve as the equation is iterated, and the specific values may depend on the starting parameters. An example is the well-studied logistic map, x n + 1 = r x n ( 1 − x n ) {\displaystyle x_{n+1}=rx_{n}(1-x_{n})}, whose basins of attraction for various values of the parameter r r are shown in the figure. If r = 2.6 {\displaystyle r=2.6}, all starting x x values of x < 0 x<0 will rapidly lead to function values that go to negative infinity; starting x x values of x > 1 x>1 will also go to negative infinity. But for 0 < x < 1 0<x<1 the x x values rapidly converge to x ≈ 0.615 {\displaystyle x\approx 0.615}, i.e. at this value of r r, a single value of x x is an attractor for the function's behaviour. For other values of r r, more than one value of x x may be visited: if r r is 3.2, starting values of 0 < x < 1 0<x<1 will lead to function values that alternate between x ≈ 0.513 {\displaystyle x\approx 0.513} and x ≈ 0.799 {\displaystyle x\approx 0.799}. At some values of r r, the attractor is a single point (a "fixed point"), at other values of r r two values of x x are visited in turn (a period-doubling bifurcation), or, as a result of furt
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Prompt:
The parameters of a dynamic equation evolve as the equation is iterated, and the specific values may depend on the starting parameters. An example is the well-studied logistic map, x n + 1 = r x n ( 1 − x n ) {\displaystyle x_{n+1}=rx_{n}(1-x_{n})}, whose basins of attraction for various values of the parameter r r are shown in the figure. If r = 2.6 {\displaystyle r=2.6}, all starting x x values of x < 0 x<0 will rapidly lead to function values that go to negative infinity; starting x x values of x > 1 x>1 will also go to negative infinity. But for 0 < x < 1 0<x<1 the x x values rapidly converge to x ≈ 0.615 {\displaystyle x\approx 0.615}, i.e. at this value of r r, a single value of x x is an attractor for the function's behaviour. For other values of r r, more than one value of x x may be visited: if r r is 3.2, starting values of 0 < x < 1 0<x<1 will lead to function values that alternate between x ≈ 0.513 {\displaystyle x\approx 0.513} and x ≈ 0.799 {\displaystyle x\approx 0.799}. At some values of r r, the attractor is a single point (a "fixed point"), at other values of r r two values of x x are visited in turn (a period-doubling bifurcation), or, as a result of furt
Modifiers:
elegant
extremely detailed
intricate
oil on canvas
photorealistic
beautiful
high detail
dynamic lighting
hyperrealistic
high definition
crisp quality
coherent
serene
graceful
4k HDR
Dream Level: is increased each time when you "Go Deeper" into the dream. Each new level is harder to achieve and
takes more iterations than the one before.
Rare Deep Dream: is any dream which went deeper than level 6.
Deep Dream
You cannot go deeper into someone else's dream. You must create your own.
Deep Dream
Currently going deeper is available only for Deep Dreams.
Artist
