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Description
Elegant Automation: Robotic Analysis of Chaotic SystemsThis book was mostly written by a machine that was programmed to search a system of equations for chaotic solutions, simplify the equations to the extent possible, analyze the behavior, produce figures, and write the accompanying text. The equations are coupled autonomous ordinary differential equations with three variables and at least one nonlinearity. Fifty simple systems are included. Some are old and familiar; others are relatively new and
This book was mostly written by a machine that was programmed to search a system of equations for chaotic solutions, simplify the equations to the extent possible, analyze the behavior, produce figures, and write the accompanying text. The equations are coupled autonomous ordinary differential equations with three variables and at least one nonlinearity. Fifty simple systems are included. Some are old and familiar; others are relatively new and unknown. They are chosen to illustrate by simple example most of dynamical behaviors that can occur in low-dimensional chaotic systems.
There is no substitute for the thrill and insight of seeing the solution of a simple equation unfold as the trajectory wanders in real time across your computer screen using a program of your own making. A goal of this book is to inspire and delight as well as to teach. It provides a wealth of examples ripe for further study and extension, and it offers a glimpse of a future when artificial intelligence supplants many of the mundane tasks that accompany dynamical systems research and becomes a true and tireless collaborator.
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4.6 ★★★★★
Based on 28 reviews
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Product Reviews
★★★★★ 5
Best vanilla body wash I've seen
Proper vanilla scent with a kick, without the vomit inducing synthetic aftertaste
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Reviewed in the United States on May 26, 2026
★★★★★ 5
A major upgrade from standard drugstore brands—sophisticated scent & better lather.
I have been a long-time user of standard body washes (think Old Spice, Axe, or Dove Men), but I kept seeing hype about Cremo and decided to see if it was worth the slightly higher price tag. After using the 32oz Spice & Black Vanilla for a week, I can confidently say this is a massive upgrade for your shower routine.
Here is how it stacks up against the typical grocery store brands:
1. The Scent is on another level:
Most cheaper washes smell like generic "Sport" or "Ocean" cologne. This scent is much more complex and earthy.
Top Notes: It starts with a sharp, spicy kick (that's the cardamom).
Finish: It settles into a smooth, warm vanilla and tobacco scent. It smells more like a high-end department store fragrance than a soap.
Staying Power: The scent actually lingers. If you shower in the morning, you will still catch subtle hints of the warm spices for a few hours, which pairs really well with woody colognes.
2. Performance & Feel:
The consistency is thicker than what I'm used to. You only need one solid pump to get a rich lather with a loofah. Crucially, it rinses clean without leaving that "squeaky" residue that dries out your skin, but it also doesn't leave a slick oily film like some ultra-moisturizing washes do. It hits a perfect balance.
3. Value:
The 32oz bottle is substantial. Because the gel is concentrated, I expect this bottle to last 3-4 months easily, making the cost per ounce very reasonable compared to buying smaller bottles of cheaper stuff every few weeks.
Pros:
Sophisticated, "grown-up" scent profile.
High-quality pump (sturdy, doesn't clog).
Non-drying formula is great for colder months.
Cons:
Potency: The scent is strong. If you are sensitive to fragrance or prefer unscented products, this might be overwhelming. The bathroom will smell like it for a good 20 minutes after you're done (which I enjoy, but keep it in mind).
Verdict:
This bridges the gap between basic hygiene and luxury grooming. If you are tired of smelling like "Blue Sport" and want something warmer and more refined for the fall/winter, this is absolutely worth the switch.
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Reviewed in the United States on November 26, 2025
★★★★★ 5
It smells as good as my cologne.
I never go out without a shot of Guerlain L'Homme Idéal L'Intense cologne. Guerlain does not offer a layered line of products with similar scents. I wanted a deodorant and body wash to match. None of the Old Spice scents came close. Axe Oud Wood & Dark Vanilla antiperspirant has more vanilla and is a bit subdued but works.
Finding a body wash was harder. Cremo Spice & Black Vanilla Body Wash sounded promising, but I was apprehensive about its scent including tobacco. I did not want to smell like an ashtray. But when I opened the bottle, I was met with a surprising scent from the past. I immediately recognized it as premium Danish pipe tobacco. Most people do not recognize this aromatic scent as coming from tobacco at all. In fact, it smells more like fresh cured tobacco itself, not its smoke. This adds a very pleasant and masculine smell to the body wash on top of the spice, wood, and vanilla scent I was searching for.
The scent only lasts a few hours after you rinse off. One push on the dispenser puts enough soap on a shower loofah to wash your whole body. I do not rinse off my loofah; I squeeze the soap out of it to wash my face, then I place it back in its tray next to the bottle. The scent of the remaining soap acts like incense until my next shower.
I was also pleasantly surprised to find that this body soap has a rich lather and cleans as well as advertised. I had forgotten the reason I bought the body soap until I used it.
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Reviewed in the United States on February 27, 2026
★★★★★ 5
Intoxicating Smell!
My 'old' shower gel was getting dangerously low prompting a search for a replacement. I looked over recommendations of various sources including Amazon which led me to this Cremo product.
Over the years I've purchased just a handful of products that were either colognes, soaps of various types, or aftershaves, which really stood out for their intoxicating scent. Additionally, they might have had the incredible ability to have a lasting effect of several hours. These products stood out in a way that they also were noticed by the people around me, commenting on the great odor and inquiring as to what it was.
This Cremo product is in that category. The first time I used it clearly put it in that rare product list. Additionally, some of the other qualities of this product that others have commented on I have found to be true. A little goes a long way! You don't need to use nearly as much as some other products that I've had in order to get it to effectively wash body or hair. It truly does leave a soft feeling after using. I didn't realize how big the container would be when I purchased it, however can now say after a few weeks of using it, this is going to last me a long time! And I'm definitely pleased about that. I guess you can say that there are definitely other less-expensive products out there, but when you consider how well this product performs, it's a great buy!
If you're currently reading this, examining products for yourself, wondering if this one is for you....hesitate no longer. When this container runs out....it's definitely going to be a long while....I will definitely buy it again.
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Reviewed in the United States on January 17, 2026
★★★★★ 5
Warm base of vanilla, with a bit of spice to keep things interesting! Definitely a keeper!
First, I need to admit that Cremo is one of my “go to” brands for body wash. I love the fact that the scents are high-quality without getting into the weird “axe” arena of being able to be smelled a mile away.
The body wash has a fresh, warm, earthy smell to it. Vanilla base with a bit of spice to not make it smell like a sugar cookie. I think you all know those body washes that are just too heavy with the vanilla smell. The price for this level of body wash is spot on for what you get from a quality, moisturizing, and skin care perspective. It doesn’t dry out your skin and even the deep rich color of the gel screams quality.
This is a really great new scent from Cremo and one that I’d definitely come back to and keep in my rotation.
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Reviewed in the United States on April 25, 2026